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
This work is licensed under a Creative Commons Attribution 4.0 License.

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. $x=\frac{-6 \pm \sqrt{42}}{4}$