How do you factor and solve  x^2-8x=-3?

Mar 7, 2018

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Explanation:

Put the equation in form

${x}^{2} - 8 x + 3 = 0$

From here we have two options:

Option a) Use the solutions formula for 2nd degree equations

$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$ for a equ in the canonic form

$a {x}^{2} + b x + c = 0$

On this way: x=(8+-sqrt(64-12))/2=(8+-sqrt(4·13))/2=4+-sqrt13

Option b) complete the square

${x}^{2} - 8 x + 3 = {\left(x - 4\right)}^{2} - 16 + 3 = {\left(x - 4\right)}^{2} - 13 = \left(x - 4 + \sqrt{13}\right) \left(x - 4 - \sqrt{13}\right)$ from here the solutions are $4 \pm \sqrt{13}$