Question

Find the value of (x − 6)² if x² – 12x = 30, and x > 0.

plsss answer ​

Answer 1

65.9

Explanation:

The equation x² – 12x = 30 (x>0) promises that we can determine possible values of x if we solve the equation. So let's start there:

We can factor the equation or solve it with the quadratic equation.

Factor

x² – 12x = 30

x² – 12x - 30 = 0

I don't see an easy factor solution. One possibility is to first rewrite the equation as

(x-12)x-30 = 0

(x-6)^2 - 66 = 0

-(-x+
`\sqrt66}`+6)(x+
`√(66)`-6)

The roots are:

x = 6-
`√(66)` and

x = 6+
`√(66)`

Since x>0, only the second root is valid: x = 6+
`√(66)`

x = 6 + (8.12)

x = 14.12

[That was painful]

Quadratic Equation

Solving with the quadratic equation gives values of:

14.12, and -2.12 Again, only the positive value is valid: 14.12

[The quadratic approach was far easier than factoring, in this case]

==

Since we established x = 14.12, (x − 6)² bcomes:

(14.12 − 6)²

(8.12)² = 65.9