Math / Algebra

QuestionSolve each equation by taking square roots. 1) $b^{2}=25$ 2) $x^{2}=92$ 3) $a^{2}-5=10$ 4) $4 v^{2}=72$ 5) $4 p^{2}-6=318$ 6) $-10-9 n^{2}=-658$

Studdy Solution

STEP 1

1. Each equation is a quadratic equation in the form of $ax^2 + bx + c = 0$ .
2. The goal is to isolate the squared term and then take the square root of both sides.
3. Solutions can be positive or negative since squaring either results in the same positive number.

STEP 2

1. Isolate the squared term.
2. Take the square root of both sides.
3. Solve for the variable.

STEP 3

Equation: $b^2 = 25$
Isolate the squared term (already isolated):
$b^2 = 25$

STEP 4

Take the square root of both sides:
$b = \pm \sqrt{25}$

STEP 5

Solve for $b$ :
$b = \pm 5$

STEP 6

Equation: $x^2 = 92$
Isolate the squared term (already isolated):
$x^2 = 92$

STEP 7

Take the square root of both sides:
$x = \pm \sqrt{92}$

STEP 8

Solve for $x$ :
$x = \pm \sqrt{92}$

STEP 9

Equation: $a^2 - 5 = 10$
Isolate the squared term by adding 5 to both sides:
$a^2 = 15$

STEP 10

Take the square root of both sides:
$a = \pm \sqrt{15}$

STEP 11

Solve for $a$ :
$a = \pm \sqrt{15}$

STEP 12

Equation: $4v^2 = 72$
Isolate the squared term by dividing both sides by 4:
$v^2 = 18$

STEP 13

Take the square root of both sides:
$v = \pm \sqrt{18}$

STEP 14

Solve for $v$ :
$v = \pm \sqrt{18}$

STEP 15

Equation: $4p^2 - 6 = 318$
Isolate the squared term by adding 6 to both sides:
$4p^2 = 324$
Divide both sides by 4:
$p^2 = 81$

STEP 16

Take the square root of both sides:
$p = \pm \sqrt{81}$

STEP 17

Solve for $p$ :
$p = \pm 9$

STEP 18

Equation: $-10 - 9n^2 = -658$
Isolate the squared term by adding 10 to both sides:
$-9n^2 = -648$
Divide both sides by -9:
$n^2 = 72$

STEP 19

Take the square root of both sides:
$n = \pm \sqrt{72}$

STEP 20

Solve for $n$ :
$n = \pm \sqrt{72}$
Solutions: 1) $b = \pm 5$ 2) $x = \pm \sqrt{92}$ 3) $a = \pm \sqrt{15}$ 4) $v = \pm \sqrt{18}$ 5) $p = \pm 9$ 6) $n = \pm \sqrt{72}$

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QuestionSolve each equation by taking square roots. 1) b2=25b^{2}=25b2=25 2) x2=92x^{2}=92x2=92 3) a2−5=10a^{2}-5=10a2−5=10 4) 4v2=724 v^{2}=724v2=72 5) 4p2−6=3184 p^{2}-6=3184p2−6=318 6) −10−9n2=−658-10-9 n^{2}=-658−10−9n2=−658

Studdy Solution

STEP 1

1. Each equation is a quadratic equation in the form of ax2+bx+c=0 ax^2 + bx + c = 0 ax2+bx+c=0.2. The goal is to isolate the squared term and then take the square root of both sides.3. Solutions can be positive or negative since squaring either results in the same positive number.

STEP 2

1. Isolate the squared term.2. Take the square root of both sides.3. Solve for the variable.

STEP 3

Equation: b2=25 b^2 = 25 b2=25Isolate the squared term (already isolated):b2=25 b^2 = 25 b2=25

STEP 4

Take the square root of both sides:b=±25 b = \pm \sqrt{25} b=±25​

STEP 5

Solve for b b b:b=±5 b = \pm 5 b=±5

STEP 6

Equation: x2=92 x^2 = 92 x2=92Isolate the squared term (already isolated):x2=92 x^2 = 92 x2=92

STEP 7

Take the square root of both sides:x=±92 x = \pm \sqrt{92} x=±92​

STEP 8

Solve for x x x:x=±92 x = \pm \sqrt{92} x=±92​

STEP 9

Equation: a2−5=10 a^2 - 5 = 10 a2−5=10Isolate the squared term by adding 5 to both sides:a2=15 a^2 = 15 a2=15

STEP 10

Take the square root of both sides:a=±15 a = \pm \sqrt{15} a=±15​

STEP 11

Solve for a a a:a=±15 a = \pm \sqrt{15} a=±15​

STEP 12

Equation: 4v2=72 4v^2 = 72 4v2=72Isolate the squared term by dividing both sides by 4:v2=18 v^2 = 18 v2=18

STEP 13

Take the square root of both sides:v=±18 v = \pm \sqrt{18} v=±18​

STEP 14

Solve for v v v:v=±18 v = \pm \sqrt{18} v=±18​

STEP 15

Equation: 4p2−6=318 4p^2 - 6 = 318 4p2−6=318Isolate the squared term by adding 6 to both sides:4p2=324 4p^2 = 324 4p2=324Divide both sides by 4:p2=81 p^2 = 81 p2=81

STEP 16

Take the square root of both sides:p=±81 p = \pm \sqrt{81} p=±81​

STEP 17

Solve for p p p:p=±9 p = \pm 9 p=±9

STEP 18

Equation: −10−9n2=−658 -10 - 9n^2 = -658 −10−9n2=−658Isolate the squared term by adding 10 to both sides:−9n2=−648 -9n^2 = -648 −9n2=−648Divide both sides by -9:n2=72 n^2 = 72 n2=72

STEP 19

Take the square root of both sides:n=±72 n = \pm \sqrt{72} n=±72​

STEP 20

Solve for n n n:n=±72 n = \pm \sqrt{72} n=±72​ Solutions: 1) b=±5 b = \pm 5 b=±5 2) x=±92 x = \pm \sqrt{92} x=±92​ 3) a=±15 a = \pm \sqrt{15} a=±15​ 4) v=±18 v = \pm \sqrt{18} v=±18​ 5) p=±9 p = \pm 9 p=±9 6) n=±72 n = \pm \sqrt{72} n=±72​

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QuestionSolve each equation by taking square roots. 1) $b^{2}=25$ 2) $x^{2}=92$ 3) $a^{2}-5=10$ 4) $4 v^{2}=72$ 5) $4 p^{2}-6=318$ 6) $-10-9 n^{2}=-658$

1. Each equation is a quadratic equation in the form of $ax^2 + bx + c = 0$ .
2. The goal is to isolate the squared term and then take the square root of both sides.
3. Solutions can be positive or negative since squaring either results in the same positive number.

1. Isolate the squared term.
2. Take the square root of both sides.
3. Solve for the variable.

Equation: $b^2 = 25$
Isolate the squared term (already isolated):
$b^2 = 25$

Take the square root of both sides:
$b = \pm \sqrt{25}$

Solve for $b$ :
$b = \pm 5$

Equation: $x^2 = 92$
Isolate the squared term (already isolated):
$x^2 = 92$

Take the square root of both sides:
$x = \pm \sqrt{92}$

Solve for $x$ :
$x = \pm \sqrt{92}$

Equation: $a^2 - 5 = 10$
Isolate the squared term by adding 5 to both sides:
$a^2 = 15$

Take the square root of both sides:
$a = \pm \sqrt{15}$

Solve for $a$ :
$a = \pm \sqrt{15}$

Equation: $4v^2 = 72$
Isolate the squared term by dividing both sides by 4:
$v^2 = 18$

Take the square root of both sides:
$v = \pm \sqrt{18}$

Solve for $v$ :
$v = \pm \sqrt{18}$

Equation: $4p^2 - 6 = 318$
Isolate the squared term by adding 6 to both sides:
$4p^2 = 324$
Divide both sides by 4:
$p^2 = 81$

Take the square root of both sides:
$p = \pm \sqrt{81}$

Solve for $p$ :
$p = \pm 9$

Equation: $-10 - 9n^2 = -658$
Isolate the squared term by adding 10 to both sides:
$-9n^2 = -648$
Divide both sides by -9:
$n^2 = 72$

Take the square root of both sides:
$n = \pm \sqrt{72}$

Solve for $n$ :
$n = \pm \sqrt{72}$
Solutions: 1) $b = \pm 5$ 2) $x = \pm \sqrt{92}$ 3) $a = \pm \sqrt{15}$ 4) $v = \pm \sqrt{18}$ 5) $p = \pm 9$ 6) $n = \pm \sqrt{72}$