Solve the Quadratic Equation: x²+10x+21=0 Step by Step

To solve this quadratic equation $x^2 + 10x + 21 = 0$, we will use the quadratic formula. Follow these steps:

• Identify the coefficients: $a = 1$, $b = 10$, $c = 21$.
• Calculate the discriminant $\Delta = b^2 - 4ac = 10^2 - 4 \cdot 1 \cdot 21 = 100 - 84 = 16$.
• The discriminant is positive, suggesting the equation has two distinct real roots.
• Apply the quadratic formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} = \frac{-10 \pm \sqrt{16}}{2 \cdot 1} = \frac{-10 \pm 4}{2}.$
• Calculate the roots:
  • First root: $x_1 = \frac{-10 + 4}{2} = \frac{-6}{2} = -3$.
  • Second root: $x_2 = \frac{-10 - 4}{2} = \frac{-14}{2} = -7$.

Therefore, the solutions to the equation are $x_1 = -3$ and $x_2 = -7$.

Comparing with the answer choices, the correct choice is $x_1 = -3, x_2 = -7$.