Answer:
x = 4, x = 8
Step-by-step explanation:
Given the quadratic equation, x² - 12x + 38 = 6
Subtract 38 from both sides:
x² - 12x + 38 - 38 = 6 - 38
x² - 12x = -32
You'll need to rewrite the equation in the form, x² + 2ax + a². To find the value of a:
2ax = -12x
Divide both sides by 2x to solve for the value of a :
[tex]\frac{2ax}{2x} = \frac{-12x}{2x}[/tex]
a = -6
Substitute the value of a into the quadratic form, x² + 2ax + a²
x² - 12x + a² = -32 + a²
x² - 12x + (-6)² = -32 + (-6)²
x² - 12x + 36 = -32 + 36
x² - 12x + 36 = 4
Rewrite the perfect square trinomial into its binomial factors:
x² - 12x + 36 = 4
(x - 6)² = 4
To solve for x, take the square root of each side of the inequality:
[tex]\sqrt{(x - 6)^{2}} = +/- \sqrt{4}[/tex]
[tex]\sqrt{(x - 6)^{2}} = \sqrt{2^{2} } = (x - 6) = 2[/tex]
For (x - 6) = 2, start by adding 6 to both sides of the equation:
x - 6 + 6 = 2 + 6
x = 8
[tex]\sqrt{(x - 6)^{2}} = -\sqrt{2^{2} } = (x - 6) = -2[/tex]
For (x - 6) = - 2, start by adding 6 to both sides of the equation:
x - 6 + 6 = - 2 + 6
x = 4
Therefore, the solutions to the quadratic equations using the perfect square strategy are: x = 4, x = 8.
