# How do you solve  x^2-4x-7=0?

Jun 4, 2016

$x = 5.317 \mathmr{and} x = - 1.317$

#### Explanation:

This is a quadratic equation. There are 3 methods for solving them:
Factorise, completing the square or using the quadratic formula.

The given equation does not factorise, so option 1 falls away.

My choice would be completing the square because:
the coefficient of ${x}^{2}$ is 1, and the coefficient of the middle term is even,

Student often think completing the square is difficult, but in a case like this it is quicker and easier than using the formula.

${x}^{2} - 4 x - 7 = 0$
Move the constant to the RHS: ${x}^{2} - 4 x \text{ } = 7$

Add on the square of, half of the middle coefficient to both sides:
( 4÷ 2 = 2 and 2^2 = 4)

${x}^{2} - 4 x + \textcolor{red}{4} = 7 + \textcolor{red}{4}$

The LHS is now the square of a binomial

${\left(x - 2\right)}^{2} = 11 \text{ }$ Now find the square root of each side

$x - 2 = \pm \sqrt{11} \text{ }$ Solve for x twice.

$x = \sqrt{11} + 2 \text{ } \mathmr{and} x = - \sqrt{11} + 2$

$x = 5.317 \text{ } \mathmr{and} x = - 1.317$