Solved on Feb 28, 2024

Find the solutions to the quadratic equation $(t+7)(t-9)=0$ . The solution set is $-7, 9$ .

STEP 1

Assumptions
1. We are given a quadratic equation in factored form: $(t+7)(t-9)=0$ .
2. To find the solutions, we need to set each factor equal to zero and solve for $t$ .

STEP 2

Set the first factor equal to zero and solve for $t$ .
$t + 7 = 0$

STEP 3

Subtract 7 from both sides of the equation to isolate $t$ .
$t = -7$

STEP 4

Set the second factor equal to zero and solve for $t$ .
$t - 9 = 0$

STEP 5

Add 9 to both sides of the equation to isolate $t$ .
$t = 9$

STEP 6

List the solutions obtained from the factors.
The solution set is $\{-7, 9\}$ .

STEP 7

Check the solutions by substituting them back into the original equation.
First, check $t = -7$ :
$(t+7)(t-9) = (-7+7)(-7-9) = 0(-16) = 0$

STEP 8

Now, check $t = 9$ :
$(t+7)(t-9) = (9+7)(9-9) = 16(0) = 0$

STEP 9

Since both checks result in the equation being true, the solutions are verified.
The solution set is $-7, 9$ .

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Find the solutions to the quadratic equation $(t+7)(t-9)=0$ . The solution set is $-7, 9$ .

STEP 1

Assumptions
1. We are given a quadratic equation in factored form: $(t+7)(t-9)=0$ .
2. To find the solutions, we need to set each factor equal to zero and solve for $t$ .

STEP 2

Set the first factor equal to zero and solve for $t$ .
$t + 7 = 0$

STEP 3

Subtract 7 from both sides of the equation to isolate $t$ .
$t = -7$

STEP 4

Set the second factor equal to zero and solve for $t$ .
$t - 9 = 0$

STEP 5

Add 9 to both sides of the equation to isolate $t$ .
$t = 9$

STEP 6

List the solutions obtained from the factors.
The solution set is $\{-7, 9\}$ .

STEP 7

Check the solutions by substituting them back into the original equation.
First, check $t = -7$ :
$(t+7)(t-9) = (-7+7)(-7-9) = 0(-16) = 0$

STEP 8

Now, check $t = 9$ :
$(t+7)(t-9) = (9+7)(9-9) = 16(0) = 0$

STEP 9

Since both checks result in the equation being true, the solutions are verified.
The solution set is $-7, 9$ .

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Find the solutions to the quadratic equation (t+7)(t−9)=0(t+7)(t-9)=0(t+7)(t−9)=0. The solution set is −7,9-7, 9−7,9.

STEP 1

Assumptions1. We are given a quadratic equation in factored form: (t+7)(t−9)=0(t+7)(t-9)=0(t+7)(t−9)=0.2. To find the solutions, we need to set each factor equal to zero and solve for ttt.

STEP 2

Set the first factor equal to zero and solve for ttt.t+7=0t + 7 = 0t+7=0

STEP 3

Subtract 7 from both sides of the equation to isolate ttt.t=−7t = -7t=−7

STEP 4

Set the second factor equal to zero and solve for ttt.t−9=0t - 9 = 0t−9=0

STEP 5

Add 9 to both sides of the equation to isolate ttt.t=9t = 9t=9

STEP 6

List the solutions obtained from the factors.The solution set is {−7,9}\{-7, 9\}{−7,9}.

STEP 7

Check the solutions by substituting them back into the original equation.First, check t=−7t = -7t=−7:(t+7)(t−9)=(−7+7)(−7−9)=0(−16)=0(t+7)(t-9) = (-7+7)(-7-9) = 0(-16) = 0(t+7)(t−9)=(−7+7)(−7−9)=0(−16)=0

STEP 8

Now, check t=9t = 9t=9:(t+7)(t−9)=(9+7)(9−9)=16(0)=0(t+7)(t-9) = (9+7)(9-9) = 16(0) = 0(t+7)(t−9)=(9+7)(9−9)=16(0)=0

STEP 9

Since both checks result in the equation being true, the solutions are verified.The solution set is −7,9-7, 9−7,9.

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

Find the solutions to the quadratic equation $(t+7)(t-9)=0$ . The solution set is $-7, 9$ .

Assumptions
1. We are given a quadratic equation in factored form: $(t+7)(t-9)=0$ .
2. To find the solutions, we need to set each factor equal to zero and solve for $t$ .

Set the first factor equal to zero and solve for $t$ .
$t + 7 = 0$

Subtract 7 from both sides of the equation to isolate $t$ .
$t = -7$

Set the second factor equal to zero and solve for $t$ .
$t - 9 = 0$

Add 9 to both sides of the equation to isolate $t$ .
$t = 9$

List the solutions obtained from the factors.
The solution set is $\{-7, 9\}$ .

Check the solutions by substituting them back into the original equation.
First, check $t = -7$ :
$(t+7)(t-9) = (-7+7)(-7-9) = 0(-16) = 0$

Now, check $t = 9$ :
$(t+7)(t-9) = (9+7)(9-9) = 16(0) = 0$

Since both checks result in the equation being true, the solutions are verified.
The solution set is $-7, 9$ .