Algebra - Quadratic Equations - Part I (Practice Problems)

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Section 2.5 : Quadratic Equations - Part I

For problems 1 – 7 solve the quadratic equation by factoring.

\({u^2} - 5u - 14 = 0\) Solution
\({x^2} + 15x = - 50\) Solution
\({y^2} = 11y - 28\) Solution
\(19x = 7 - 6{x^2}\) Solution
\(6{w^2} - w = 5\) Solution
\({z^2} - 16z + 61 = 2z - 20\) Solution
\(12{x^2} = 25x\) Solution

For problems 8 & 9 use factoring to solve the equation.

\({x^4} - 2{x^3} - 3{x^2} = 0\) Solution
\({t^5} = 9{t^3}\) Solution

For problems 10 – 12 use factoring to solve the equation.

\(\displaystyle \frac{{{w^2} - 10}}{{w + 2}} + w - 4 = w - 3\) Solution
\(\displaystyle \frac{{4z}}{{z + 1}} + \frac{5}{z} = \frac{{6z + 5}}{{{z^2} + z}}\) Solution
\(\displaystyle x + 1 = \frac{{2x - 7}}{{x + 5}} - \frac{{5x + 8}}{{x + 5}}\) Solution

For problems 13 – 16 use the Square Root Property to solve the equation.

\(9{u^2} - 16 = 0\) Solution
\({x^2} + 15 = 0\) Solution
\({\left( {z - 2} \right)^2} - 36 = 0\) Solution
\({\left( {6t + 1} \right)^2} + 3 = 0\) Solution