Solve the equation 8, x, minus, 27, equals, minus, 2, x, squared8x−27=−2x 2 to the nearest tenth.

The given equation is 8x - 27 = -2x^2.

Step 1: Rearrange the equation to set it equal to zero. This gives us 2x^2 + 8x - 27 = 0.

Step 2: This is a quadratic equation in the form ax^2 + bx + c = 0. We can solve it using the quadratic formula, x = [-b ± sqrt(b^2 - 4ac)] / (2a).

Step 3: Substitute a = 2, b = 8, and c = -27 into the quadratic formula. This gives us x = [-8 ± sqrt((8)^2 - 42(-27))] / (2*2).

Step 4: Simplify the equation under the square root to get x = [-8 ± sqrt(64 + 216)] / 4.

Step 5: Further simplify to get x = [-8 ± sqrt(280)] / 4.

Step 6: Calculate the square root to get x = [-8 ± 16.73] / 4.

Step 7: Solve for x to get two possible solutions: x = (-8 + 16.73) / 4 = 2.2 and x = (-8 - 16.73) / 4 = -6.2.

So, the solutions to the equation 8x - 27 = -2x^2 are x = 2.2 and x = -6.2.