Question

1. what is the greatest solution of ( x ) in the equation ( x^2 + 8x - 30 = 18 )? enter your answer in the box.

Explanation:

Step1: Rearrange to standard quadratic form

Subtract 18 from both sides to set the equation to 0:
$x^2 + 8x - 30 - 18 = 0$
$x^2 + 8x - 48 = 0$

Step2: Factor the quadratic equation

Find two numbers that multiply to -48 and add to 8 (12 and -4):
$(x + 12)(x - 4) = 0$

Step3: Solve for x

Set each factor equal to 0:
$x + 12 = 0 \implies x = -12$
$x - 4 = 0 \implies x = 4$

Step4: Identify the greatest solution

Compare the two solutions: $4 > -12$

Answer:

4