How do you solve $x^{2} + x - 20 = 0$ $x^2+x-20=0$ ?

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How do you solve $x^{2} + x - 20 = 0$ $x^2+x-20=0$ ?

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Answer 1 · 2016-03-28T14:09:04

$x = 4, - 5$ $x=4,-5$

Explanation:

$x^{2} + x - 20 = 0$ $color(blue)(x^2+x-20=0$

First, Factor the equation:

$\to x^{2} + 5 x - 4 x - 20 = 0$ $rarrx^2+5x-4x-20=0$

$\to x (x + 5) - 4 (x + 5) = 0$ $rarrx(x+5)-4(x+5)=0$

$\to (x - 4) (x + 5) = 0$ $color(purple)(rarr(x-4)(x+5)=0$

$\approx \approx \approx \approx \approx \approx \approx \approx \approx \approx \approx \approx \approx \approx \approx \approx \approx \approx$ $~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~$

Next, set both equations equal to zero, and solve.

$\to x - 4 = 0$ $rarrx-4=0$

Add four to each side, and solve:

$rarrxcancel(-4+4)=0+4$

$color(green)(rArrx=4$

$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~$

$rarrx+5=0$

Subtract $5$ from each side, and solve:

$rarrxcancel(+5-5)=0-5$

$color(green)(rArrx=-5$

$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~$

$:.color(indigo)( ul bar |x=4, -5|$

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How do you solve $x^{2} + x - 20 = 0$ $x^2+x-20=0$ ?

1 Answer

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