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How do you solve $x^2-10x+8=0$ using the quadratic formula?

1 Answer

Feb 29, 2016

$x=5+-sqrt(17)$

Explanation:

$1$ . Determine the $a$ , $b$ , and $c$ values of the equation. Recall that the general quadratic equation written in standard form is: $ax^2+bx+c=0$ .

$x^2-10x+8=0$

$color(red)(1)x^2$ $color(orange)(-10)x$ $color(blue)(+8)=0$

$a=color(red)1color(white)(XXX)b=color(orange)(-10)color(white)(XXX)c=color(blue)(8)$

$2$ . Substitute the $a$ , $b$ , and $c$ values into the quadratic formula.

$x=(-b+-sqrt(b^2-4ac))/(2a)$

$x=(-(color(orange)(-10))+-sqrt((color(orange)(-10))^2-4(color(red)1)(color(blue)8)))/(2(color(red)1))$

$3$ . Solve for $x$ .

$x=(10+-sqrt(100-32))/2$

$x=(10+-sqrt(68))/2$

$x=(10+-2sqrt(17))/2$

$x=(2(5+-sqrt(17)))/(2(1))$

$x=(color(red)cancelcolor(black)2(5+-sqrt(17)))/(color(red)cancelcolor(black)2(1))$

$color(green)(x=5+-sqrt(17))$

$:.$ , $x=5+-sqrt(17)$ .

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