Solve the equation minus, x, squared, plus, 4, x, plus, 2, equals, minus, 2, x, squared−x 2 +4x+2=−2x 2 to the nearest tenth.

The given equation is -x^2 + 4x + 2 = -2x^2.

First, let's simplify the equation by adding x^2 to both sides to get rid of the negative x^2 on the left side:

-x^2 + x^2 + 4x + 2 = -2x^2 + x^2 This simplifies to: 4x + 2 = -x^2

Next, let's rearrange the equation to set it equal to zero:

x^2 + 4x + 2 = 0

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

In this equation, a = 1, b = 4, and c = 2.

Substituting these values into the quadratic formula gives:

x = [-4 ± sqrt((4)^2 - 412)] / (2*1) x = [-4 ± sqrt(16 - 8)] / 2 x = [-4 ± sqrt(8)] / 2 x = [-4 ± 2.83] / 2

This gives us two possible solutions:

x = (-4 + 2.83) / 2 = -0.6 (to the nearest tenth) x = (-4 - 2.83) / 2 = -3.4 (to the nearest tenth)

So, the solutions to the equation are x = -0.6 and x = -3.4.