Question

(x − 2)(x + 6) = 1 Solve the quadratic equation. Give both the exact form of the answer and a calculator approximation rounded to two decimal places.

Answer 1

on simplifying the equation you get,
x^2 + 4x - 12 = 1
x^2 + 4x -12 -1 = 0
x^2 + 4x - 13 = 0
now you can use the
formula,
\[\left( \frac{ -b \pm \sqrt{b^2 - 4ac} }{ 2a } \right)\]
i got
2.12 and -6.12

Answer 2

What were your calculations to get 2.12 and -6.12?

Answer 3

(x-2)(x+6) = 1
x(x+6) - 2(x+6) = 1
x^2 + 6x - 2x - 12 = 1
x^2 +4x - 12 = 1
x^2 + 4x - 13 =0

(2 + d)(2 - d) = -13
4 - d^2 = -13
4 + 13 = d^2
17 = d^2
sqrt{17} = d

(2 + sqrt{17})(2 - sqrt{17}) = -13
2 + sqrt{17} + 2 - sqrt{17} = 4

x^2 + 2 + sqrt{17}x + 2 - sqrt{17}x - 13 = 0
x(x + 2 + sqrt{17}) + 2-sqrt{17}(x + 2 + sqrt{17}) = 0
(x + 2 + sqrt{17})(x + 2 - sqrt{17}) = 0

x = -2 - sqrt{17}
x = -2 + sqrt{-17}

That's the exact solution

Answer 4

@danieljkim12

Answer 5

Very well, thank you so much!

Answer 6

Good luck understanding the steps