How do you solve by completing the square: $x^2=8x+10$ ?

Question

13530 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-07-07T07:09:42

$x = 4+- sqrt(26)$

Given: $x^2 = 8x + 10$ . Solve using completing of the square.

First, group the monomials with $x$ together on the same side:

$x^2 - 8x = 10$

To complete the square, multiply the constant of the $x$ monomial by $1/2$ : $" "-8 *1/2 = -8/2 = -4$

When you complete the square you end up adding a square term:
$(a + b)^2 = a^2 + 2ab + b^2$

$(x - 4)^2 = x^2 - 8x + color(red)( (-4)^2)$

This term must be also added to the right side of the equation:

$(x - 4)^2 = 10 + (-4)^2$

$(x-4)^2 = 26$

Square root both sides:

$x - 4 = +- sqrt(26)$

$x = 4 +- sqrt(26)$

How do you solve by completing the square: x^2=8x+10x^2=8x+10?