# How do you solve x^2+9=10x?

Apr 11, 2016

1 and 9

#### Explanation:

$y = {x}^{2} - 10 x + 9 = 0.$
Find 2 real roots, knowing sum (-b = 10) and product (c = 9).
They are 1 and 9.

Apr 11, 2016

$9 , 1$

#### Explanation:

color(blue)(x^2+9=10x

Subtract $10 x$ both sides

rarrx^2+9-10x=cancel(10x-10x

$\rightarrow {x}^{2} + 9 - 10 x = 0$

Rewrite the equation in Standard form ($a {x}^{2} + b x + c = 0$)

color(purple)(rarrx^2-10x+9=0

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

Remember that $a \mathmr{and} b$ are the coefficients and $c$ is the constant

So,

color(violet)(a=1

color(violet)(b=-10

color(violet)(c=9

$\rightarrow x = \frac{- \left(- 10\right) \pm \sqrt{- {10}^{2} - 4 \left(1\right) \left(9\right)}}{2 \left(1\right)}$

$\rightarrow x = \frac{10 \pm \sqrt{100 - \left(36\right)}}{2}$

$\rightarrow x = \frac{10 \pm \sqrt{64}}{2}$

$\rightarrow x = \frac{10 \pm 8}{2}$

$\rightarrow x = \frac{{\cancel{10}}^{5} \pm {\cancel{8}}^{4}}{{\cancel{2}}^{1}}$

$\rightarrow x = 5 \pm 4$

Remember that $\pm$ means "plus or minus",

Which implies that,

color(indigo)(x=5+4=9

color(orange)(x=5-4=1

color(blue)( ul bar |x=9,1|

If you are confused with the Quadratic formula

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