QuestionSolve the equation: $a^{2}+2(b-6)-17=24$ .

Studdy Solution

STEP 1

Assumptions1. The given equation is $a^{}+(b-6)-17=24$ . We need to solve this equation for $a$ and $b$

STEP 2

First, simplify the equation by distributing the $2$ to the terms inside the parentheses.
$a^{2}+2b-12-17=24$

STEP 3

Combine like terms on the left side of the equation.
$a^{2}+2b-29=24$

STEP 4

Next, isolate $a^{2}$ by moving the other terms to the right side of the equation.
$a^{2}=24-2b+29$

STEP 5

implify the right side of the equation.
$a^{2}=53-2b$

STEP 6

To solve for $a$ , take the square root of both sides. Remember that the square root of a square is the absolute value, so we get two solutions $a=\sqrt{53-2b}$ and $a=-\sqrt{53-2b}$ .
$a=\pm\sqrt{53-2b}$ At this point, we have solved for $a$ in terms of $b$ . To solve for $b$ , we would need additional information or constraints on the values of $a$ and $b$ . Without such information, we can't solve for $b$ .

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QuestionSolve the equation: $a^{2}+2(b-6)-17=24$ .

Studdy Solution

STEP 1

Assumptions1. The given equation is $a^{}+(b-6)-17=24$ . We need to solve this equation for $a$ and $b$

STEP 2

First, simplify the equation by distributing the $2$ to the terms inside the parentheses.
$a^{2}+2b-12-17=24$

STEP 3

Combine like terms on the left side of the equation.
$a^{2}+2b-29=24$

STEP 4

Next, isolate $a^{2}$ by moving the other terms to the right side of the equation.
$a^{2}=24-2b+29$

STEP 5

implify the right side of the equation.
$a^{2}=53-2b$

STEP 6

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QuestionSolve the equation: a2+2(b−6)−17=24a^{2}+2(b-6)-17=24a2+2(b−6)−17=24.

Studdy Solution

STEP 1

Assumptions1. The given equation is a+(b−6)−17=24a^{}+(b-6)-17=24a+(b−6)−17=24 . We need to solve this equation for aaa and bbb

STEP 2

First, simplify the equation by distributing the 222 to the terms inside the parentheses.a2+2b−12−17=24a^{2}+2b-12-17=24a2+2b−12−17=24

STEP 3

Combine like terms on the left side of the equation.a2+2b−29=24a^{2}+2b-29=24a2+2b−29=24

STEP 4

Next, isolate a2a^{2}a2 by moving the other terms to the right side of the equation.a2=24−2b+29a^{2}=24-2b+29a2=24−2b+29

STEP 5

implify the right side of the equation.a2=53−2ba^{2}=53-2ba2=53−2b

STEP 6

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionSolve the equation: $a^{2}+2(b-6)-17=24$ .

Assumptions1. The given equation is $a^{}+(b-6)-17=24$ . We need to solve this equation for $a$ and $b$

First, simplify the equation by distributing the $2$ to the terms inside the parentheses.
$a^{2}+2b-12-17=24$

Combine like terms on the left side of the equation.
$a^{2}+2b-29=24$

Next, isolate $a^{2}$ by moving the other terms to the right side of the equation.
$a^{2}=24-2b+29$

implify the right side of the equation.
$a^{2}=53-2b$