Taking a Square Root to Solve an Equation

Taking a Square Root to Solve an Equation

Solve: 27 9x In order to solve for x, you have to UNDO the

squared first (i.e. square root)7x What are the

number(s) whose square

is 9?

The square of 3 AND -3

is 9

7 3x 7 3x 7 3x 10x 4x Find the x

that makes x-7 equal

POSITIVE 3

Find the x that makes x-7 equal

NEGATIVE 3

NOTE: In general, this method only works when there is ONE variable in the equation.

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Taking a Square Root to Solve an Equation

Solve: 23 12x In order to solve for x, you have to UNDO the

squared first (i.e. square root)3x What are the

number(s) whose square

is 12?

Do not forget the square of a positive and negative

number is positive

3 2 3x

3 2 3x 3 2 3x

3 2 3x 3 2 3x Find the x that makes x-3 equal a POSITIVE

Find the x that makes x-3 equal a NEGATIVE

Simplify any square roots

3 2 3x Is also an acceptable EXACT answer

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0.464 6.464x orAre acceptable APPROXIMATE answers

EXACT answers

Taking a Square Root to Solve an Equation

Solve: 22 11x In order to solve for x, you have to UNDO the

squared first (i.e. square root)2x What are the

number(s) whose square

is -11?

NOT POSSIBLE

The square of a number can not be negative.

This equation has NO SOLUTIONS.

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Taking a Square Root to Solve an Equation

Solve: 25 10 0x In order to solve for x, you have to UNDO the

squared first (i.e. square root)5 10x What are the

number(s) whose square

is 0?

The square of 0 AND -0

is 0

5 10 0x

5 10 0x

12x

Since +0 and -0 are the

same number.

There is only ONE

Answer.

0

10 5x