Solve the equation minus, x, squared, plus, 9, x, minus, 26, equals, minus, 2, x, squared, plus, 24−x 2 +9x−26=−2x 2 +24 to the nearest tenth.

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

Given equation: $-x^2 + 9x - 26 = -2x^2 + 24$

Step 1: Move all terms to one side of the equation to set it to zero. $-x^2 + 9x - 26 + 2x^2 - 24 = 0$

Step 2: Combine like terms. $(-x^2 + 2x^2) + 9x + (-26 - 24) = 0$ $x^2 + 9x - 50 = 0$

Step 3: Use the quadratic formula to solve for $x$. The quadratic formula is: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ where $a = 1$, $b = 9$, and $c = -50$.

Step 4: Substitute the values of $a$, $b$, and $c$ into the quadratic formula. $x = \frac{-9 \pm \sqrt{9^2 - 4 \cdot 1 \cdot (-50)}}{2 \cdot 1}$ $x = \frac{-9 \pm \sqrt{81 + 200}}{2}$ $x = \frac{-9 \pm \sqrt{281}}{2}$

Step 5: Calculate the discriminant. $\sqrt{281} \approx 16.8$

Step 6: Solve for the two possible values of $x$. $x = \frac{-9 + 16.8}{2} \approx \frac{7.8}{2} \approx 3.9$ $x = \frac{-9 - 16.8}{2} \approx \frac{-25.8}{2} \approx -12.9$

So, the solutions to the equation, rounded to the nearest tenth, are: $x \approx 3.9 \quad \text{and} \quad x \approx -12.9$