Solve the equation x, squared, plus, 20, x, plus, 26, equals, minus, 2, x, squaredx 2 +20x+26=−2x 2 to the nearest tenth.

Sure, let's solve the equation step by step.

Given equation: $x^2 + 20x + 26 = -2x^2$

Step 1: Move all terms to one side of the equation to set it to zero. $x^2 + 20x + 26 + 2x^2 = 0$

Step 2: Combine like terms. $3x^2 + 20x + 26 = 0$

Step 3: Use the quadratic formula to solve for $x$. The quadratic formula is: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ where $a = 3$, $b = 20$, and $c = 26$.

Step 4: Calculate the discriminant ($\Delta$). $\Delta = b^2 - 4ac$ $\Delta = 20^2 - 4(3)(26)$ $\Delta = 400 - 312$ $\Delta = 88$

Step 5: Substitute the values into the quadratic formula. $x = \frac{-20 \pm \sqrt{88}}{6}$

Step 6: Simplify the square root of 88. $\sqrt{88} \approx 9.4$

Step 7: Calculate the two possible values for $x$. $x_1 = \frac{-20 + 9.4}{6}$ $x_1 = \frac{-10.6}{6}$ $x_1 \approx -1.8$

$x_2 = \frac{-20 - 9.4}{6}$ $x_2 = \frac{-29.4}{6}$ $x_2 \approx -4.9$

So, the solutions to the equation, rounded to the nearest tenth, are: $x \approx -1.8$ $x \approx -4.9$