0. Review of College Algebra

Solving Quadratic Equations

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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.

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 3, divide it by 2 to get 3/2, and then square it to get (3/2)^2 = 9/4.

Add and subtract 9/4 inside the equation to maintain equality: x^2 + 3x + 9/4 - 9/4 = 5.

Rewrite the left side as a perfect square trinomial: (x + 3/2)^2 = 5 + 9/4, then solve for x by taking the square root of both sides and isolating x.

Master Introduction to Quadratic Equations with a bite sized video explanation from Patrick

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Expert video explanations

Solve the given quadratic equation by completing the square. x2+3x−5=0x^2+3x-5=0x2+3x−5=0