1. Equations & Inequalities

Completing the Square

1. Equations & Inequalities

Completing the Square

Struggling with College Algebra?

Join thousands of students who trust us to help them ace their exams!Watch the first video

Multiple Choice

Solve the given quadratic equation by completing the square. $x^2+3x-5=0$

$x=-\frac32,x=\frac52$

$x=-\frac32,x=\sqrt{29}$

$x=\frac{-3+\sqrt{29}}{2},x=\frac{-3-\sqrt{29}}{2}$

$x=\frac{3+\sqrt{29}}{2},x=\frac{3-\sqrt{29}}{2}$

Verified step by step guidance

Start with the quadratic equation: $ x^2 + 3x - 5 = 0 $. The goal is to complete the square to solve for $ x $.

Move the constant term to the other side of the equation: $ x^2 + 3x = 5 $.

To complete the square, take half of the coefficient of $ x $, which is $ \frac{3}{2} $, and square it: $ \left( \frac{3}{2} \right)^2 = \frac{9}{4} $.

Add $ \frac{9}{4} $ to both sides of the equation to form a perfect square trinomial on the left: $ x^2 + 3x + \frac{9}{4} = 5 + \frac{9}{4} $.

Rewrite the left side as a squared binomial: $ \left( x + \frac{3}{2} \right)^2 = \frac{29}{4} $. Now, solve for $ x $ by taking the square root of both sides and then isolating $ x $.