Answer :
Hello!
We have the equation 2x² +5x -63 = 0
First, let's find the coefficients a, b and c as ax² +bx +c = 0:
• a = 2
,• b = 5
,• c = -63
Now, we will use the formula below to solve this equation:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4\cdot a\cdot c}}{2\cdot a}[/tex]Let's replace the coefficients with the values that we already found:
[tex]\begin{gathered} x=\frac{-5\pm\sqrt[]{5^2-4\cdot2\cdot(-63)_{}}}{2\cdot2} \\ \\ x=\frac{-5\pm\sqrt[]{5^2+504_{}}}{4} \\ \\ x=\frac{-5\pm\sqrt[]{25^{}+504_{}}}{4} \\ \\ x=\frac{-5\pm\sqrt[]{529}}{4} \\ \\ x=\frac{-5\pm23}{4} \end{gathered}[/tex]Now, let's divide it into two solutions, look:
[tex]\begin{gathered} x_1=\frac{-5+23}{4}=\frac{18}{4}=\frac{9}{2} \\ \\ x_2=\frac{-5-23}{4}=-\frac{28}{4}=-7 \end{gathered}[/tex]Right answer: C) -7 is a solution.