Practice with the Quadratic Formula

Practice Makes Perfect

Solve Quadratic Equations Using the Quadratic Formula

In the following exercises, solve by using the Quadratic Formula.

99. \(4 m^{2}+m-3=0\)

101. \(2 p^{2}-7 p+3=0\)

103. \(p^{2}+7 p+12=0\)

105. \(r^{2}-8 r-33=0\)

107. \(3 u^{2}+7 u-2=0\)

109. \(2 a^{2}-6 a+3=0\)

111. \(2 x^{2}+3 x+9=0\)

113. \(v(v+5)-10=0\)

115. \(\frac{1}{3} m^{2}+\frac{1}{12} m=\frac{1}{4}\)

117. \(16 c^{2}+24 c+9=0\)

119. \(5 m^{2}+2 m-7=0\)

121. \(p^{2}-6 p-27=0\)

123. \(4 r^{2}+3 r-5=0\)

125. \(2 a^{2}+12 a+5=0\)

127.\(\frac{3}{4} b^{2}+\frac{1}{2} b=\frac{3}{8}\)

129. \(2 x^{2}+12 x-3=0\)

Source: Rice University, https://openstax.org/books/elementary-algebra-2e/pages/10-3-solve-quadratic-equations-using-the-quadratic-formula
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99. \(m=-1, m=\frac{3}{4}\)

101. \(p=\frac{1}{2}, p=3\)

103. \(p=-4, p=-3\)

105. \(r=-3, r=11\)

107. \(u=\frac{-7 \pm \sqrt{73}}{6}\)

109. \(a=\frac{3 \pm \sqrt{3}}{2}\)

111. no real solution

113. \(v=\frac{-5 \pm \sqrt{65}}{2}\)

115. \(m=-1, m=\frac{3}{4}\)

117. \(c=-\frac{3}{4}\)

119. \(m=-\frac{7}{5}, m=1\)

121. \(p=-3, p=9\)

123. \(r=\frac{-3 \pm \sqrt{89}}{8}\)

125. \(a=\frac{-6 \pm \sqrt{26}}{2}\)

127. \(b=\frac{-2 \pm \sqrt{22}}{6}\)

129. \(x=\frac{-6 \pm \sqrt{42}}{4}\)