How do you solve $x^{2} = x + 6$ $x^2 = x + 6$ ?

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How do you solve $x^{2} = x + 6$ $x^2 = x + 6$ ?

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Answer 1 · 2018-03-02T21:28:11

$x = - 2 or x = 3$ $x=-2" or "x=3$

Explanation:

$rearrange into standard form$ $"rearrange into standard form"$

$\Rightarrow x^{2} - x - 6 = 0 \leftarrow in standard form$ $rArrx^2-x-6=0larrcolor(blue)"in standard form"$

$the factors of - 6 which sum to - 1 are - 3 and + 2$ $"the factors of - 6 which sum to - 1 are - 3 and + 2"$

$\Rightarrow (x - 3) (x + 2) = 0$ $rArr(x-3)(x+2)=0$

$equate each factor to zero and solve for x$ $"equate each factor to zero and solve for x"$

$x + 2 = 0 \Rightarrow x = - 2$ $x+2=0rArrx=-2$

$x - 3 = 0 \Rightarrow x = 3$ $x-3=0rArrx=3$

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How do you solve $x^{2} = x + 6$ $x^2 = x + 6$ ?

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