If (2x - 3)^2 = 25 and x < 0, what is the value of x? — GRE General Test

If $(2x - 3)^2 = 25$ and $x < 0$ , what is the value of $x$ ?

-1

Taking the square root of both sides of

(2x - 3)^2 = 25

yields two equations:

2x - 3 = 5

(which gives

x = 4

) and

2x - 3 = -5

(which gives

x = -1

). Because the problem specifies that

x < 0

, the correct value must be

-1

Take the square root of both sides of the equation

(2x - 3)^2 = 25

2x - 3 = \pm 5

Applying the square root property to a squared binomial requires considering both positive and negative principal roots.

Set up two separate linear equations corresponding to the two cases

Case 1:

2x - 3 = 5

or Case 2:

2x - 3 = -5

To find all possible solutions for

x

, evaluate both root possibilities.

Solve each linear equation for

x

Case 1 yields

2x = 8 \implies x = 4

. Case 2 yields

2x = -2 \implies x = -1

Isolate

x

using standard algebraic operations.

Apply the given constraint

x < 0

x = -1

Since

4 > 0

, the positive root is eliminated, leaving

x = -1

as the sole valid solution.

Quadratic Equations and Factoring

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