Complete the square

Question

Equ equation has the same solution as x2 + x - 11 = 7

Answer 1

The idea in completing the square is rewriting the given equation as as square . To do so, you need to add or subtract constants from both sides of the equation.

In this case we have x^{2 -} x - 11 = 7. . We note that x^{2 -} x +1/4 = ( x - 1/2)²

Using this information, we can rewrite the original equation as ( x - 1/2)2 - 1/4 - 11 = 7

Probably easiest to solve if you put the numbers on the right hand side.

( x - 1/2)^{2 =} = 7 + 11+ 1/4 = 18 1/4

x = sqrt(18 1/4) + 1/2