What are the solutions of the equation (x + 2)2 + 12(x + 2) – 14 = 0? Use u substitution and the quadratic formula to solve x=-8+55

Question

What are the solutions of the equation (x + 2)2 + 12(x + 2) – 14 = 0? Use u substitution and the quadratic formula to solve
x=-8+55
x–653
X=-45_2
x = -2+52

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Cora 2 weeks 2021-09-13T11:06:20+00:00 1 Answer 0

Answers ( )

    0
    2021-09-13T11:08:12+00:00

    Answer:

    \large\boxed{x=-8\pm5\sqrt2}

    Step-by-step explanation:

    (x-2)^2+12(x+2)-14=0\\\\\text{Substitute}\ (x+2)=t:\\\\t^2+12t-14=0\qquad\text{add 14 to both sides}\\\\t^2+2(t)(6)=14\qquad\text{add}\ 6^2=36\ \text{to both sides}\\\\\underbrace{t^2+2(t)(6)+6^2}=14+36\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\(t+6)^2=50\Rightarrow t+6=\pm\sqrt{50}\qquad\text{subtract 6 from both sides}\\\\t=-6\pm\sqrt{25\cdot2}\\\\t=-6\pm5\sqrt2

    \text{we're going back to substitution}\\\\x+2=-6\pm5\sqrt2\qquad\text{subtract 2 from both sides}\\\\x=-8\pm5\sqrt2

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