Question

Steve is using the completing the square method to solve a quadratic equation. His first 2 steps are shown.
Given: 2x2 + 32x + 16 = 0
Step 1: 2? + 16x +8 = 0
Step 2: ? + 160 = -8
Write numbers in each box to correctly complete the square in Step 3.
Step 3: x2 + 16x+ ____=____

Answer 1

We muss add the polynomic expression $x^{2}+16\cdot x = -8$  by 64 on both sides.

How to apply the completing the square method to solve a quadratic equation

In this question we must apply the completing the square method to solve a quadratic equation, which consists in apply algebra properties to reduce part of a expression into a square perfect trinomial.

According to the step 2, we have the following expression:

$x^{2}+16\cdot x = -8$   (1)

By applying the principle of compatibility with addition and definition of addition, we have the following expression:

$x^{2}+16\cdot x + 64 = - 8 + 64$

$x^{2}+16\cdot x +64 = 56$

Now we proceed to solve the given expression:

$(x+8)^{2} = 56$

$x+8 = \pm 2\sqrt{14}$

$x = -8 \pm 2\sqrt{14}$

We muss add the polynomic expression $x^{2}+16\cdot x = -8$  by 64 on both sides. $\blacksquare$

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