Completing the Square

${x}^{2}+4x-1 = 0$ cannot be factored with whole numbers. Completing the square still solves it.

• Move the number to the right side: ${x}^{2}+4x = 1$.
• Add the missing number, 4, to both sides: ${x}^{2}+4x+4 = 5$.
• Write the left side as a square: ${\left(x+2\right)}^{2} = 5$.
• Take the square root, with both signs: $x+2 = \sqrt{5}$ or $x+2 = -\sqrt{5}$.
• Subtract 2: $x = -2+\sqrt{5}$ or $x = -2-\sqrt{5}$.

This works for every quadratic equation, and the answers are exact.