The square of a number plus the number is 12. What is the number?

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Answer 1 · 2016-12-11T00:16:10

$x = - 4$ $x = -4$ or $x = 3$ $x = 3$

If $x$ $x$ represents the number, then we can express the given information as:

$x^{2} + x = 12$ $x^2+x=12$

Subtract $12$ $12$ from both sides to get a quadratic equation in standard form:

$x^{2} + x - 12 = 0$ $x^2+x-12 = 0$

Note that $4 \cdot 3 = 12$ $4*3 = 12$ and $4 - 3 = 1$ $4-3 = 1$ . So we find:

$(x + 4) (x - 3) = x^{2} + x - 12 = 0$ $(x+4)(x-3) = x^2+x-12 = 0$

Hence $x = - 4$ $x = -4$ or $x = 3$ $x = 3$