Solve the equation 2, x, squared, plus, 2, x, minus, 6, equals, x, squared2x 2 +2x−6=x 2 to the nearest tenth.

The equation you provided seems to be a bit unclear, but I'm assuming you meant 2x^2 + 2x - 6 = x^2. Here's how you can solve it:

Step 1: Rearrange the equation to bring all terms to one side. This gives us: 2x^2 - x^2 + 2x - 6 = 0

Step 2: Simplify the equation: x^2 + 2x - 6 = 0

Step 3: 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). Here, a = 1, b = 2, and c = -6.

Step 4: Substitute a, b, and c into the quadratic formula: x = [-2 ± sqrt((2)^2 - 41(-6))] / (21) x = [-2 ± sqrt(4 + 24)] / 2 x = [-2 ± sqrt(28)] / 2 x = [-2 ± 2sqrt(7)] / 2 x = -1 ± sqrt(7)

So, the solutions to the equation are x = -1 + sqrt(7) and x = -1 - sqrt(7). To the nearest tenth, these are approximately x = 1.6 and x = -2.6.