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Simplifying 9x * 9x + -10 = 8x * 8x + -6x Reorder the terms for easier multiplication: 9 * 9x * x + -10 = 8x * 8x + -6x Multiply 9 * 9 81x * x + -10 = 8x * 8x + -6x Multiply x * x 81x2 + -10 = 8x * 8x + -6x Reorder the terms: -10 + 81x2 = 8x * 8x + -6x Reorder the terms for easier multiplication: -10 + 81x2 = 8 * 8x * x + -6x Multiply 8 * 8 -10 + 81x2 = 64x * x + -6x Multiply x * x -10 + 81x2 = 64x2 + -6x Reorder the terms: -10 + 81x2 = -6x + 64x2 Solving -10 + 81x2 = -6x + 64x2 Solving for variable 'x'. Reorder the terms: -10 + 6x + 81x2 + -64x2 = -6x + 64x2 + 6x + -64x2 Combine like terms: 81x2 + -64x2 = 17x2 -10 + 6x + 17x2 = -6x + 64x2 + 6x + -64x2 Reorder the terms: -10 + 6x + 17x2 = -6x + 6x + 64x2 + -64x2 Combine like terms: -6x + 6x = 0 -10 + 6x + 17x2 = 0 + 64x2 + -64x2 -10 + 6x + 17x2 = 64x2 + -64x2 Combine like terms: 64x2 + -64x2 = 0 -10 + 6x + 17x2 = 0 Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. -0.5882352941 + 0.3529411765x + x2 = 0 Move the constant term to the right: Add '0.5882352941' to each side of the equation. -0.5882352941 + 0.3529411765x + 0.5882352941 + x2 = 0 + 0.5882352941 Reorder the terms: -0.5882352941 + 0.5882352941 + 0.3529411765x + x2 = 0 + 0.5882352941 Combine like terms: -0.5882352941 + 0.5882352941 = 0.0000000000 0.0000000000 + 0.3529411765x + x2 = 0 + 0.5882352941 0.3529411765x + x2 = 0 + 0.5882352941 Combine like terms: 0 + 0.5882352941 = 0.5882352941 0.3529411765x + x2 = 0.5882352941 The x term is 0.3529411765x. Take half its coefficient (0.1764705883). Square it (0.03114186853) and add it to both sides. Add '0.03114186853' to each side of the equation. 0.3529411765x + 0.03114186853 + x2 = 0.5882352941 + 0.03114186853 Reorder the terms: 0.03114186853 + 0.3529411765x + x2 = 0.5882352941 + 0.03114186853 Combine like terms: 0.5882352941 + 0.03114186853 = 0.61937716263 0.03114186853 + 0.3529411765x + x2 = 0.61937716263 Factor a perfect square on the left side: (x + 0.1764705883)(x + 0.1764705883) = 0.61937716263 Calculate the square root of the right side: 0.787005186 Break this problem into two subproblems by setting (x + 0.1764705883) equal to 0.787005186 and -0.787005186.Subproblem 1
x + 0.1764705883 = 0.787005186 Simplifying x + 0.1764705883 = 0.787005186 Reorder the terms: 0.1764705883 + x = 0.787005186 Solving 0.1764705883 + x = 0.787005186 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1764705883' to each side of the equation. 0.1764705883 + -0.1764705883 + x = 0.787005186 + -0.1764705883 Combine like terms: 0.1764705883 + -0.1764705883 = 0.0000000000 0.0000000000 + x = 0.787005186 + -0.1764705883 x = 0.787005186 + -0.1764705883 Combine like terms: 0.787005186 + -0.1764705883 = 0.6105345977 x = 0.6105345977 Simplifying x = 0.6105345977Subproblem 2
x + 0.1764705883 = -0.787005186 Simplifying x + 0.1764705883 = -0.787005186 Reorder the terms: 0.1764705883 + x = -0.787005186 Solving 0.1764705883 + x = -0.787005186 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1764705883' to each side of the equation. 0.1764705883 + -0.1764705883 + x = -0.787005186 + -0.1764705883 Combine like terms: 0.1764705883 + -0.1764705883 = 0.0000000000 0.0000000000 + x = -0.787005186 + -0.1764705883 x = -0.787005186 + -0.1764705883 Combine like terms: -0.787005186 + -0.1764705883 = -0.9634757743 x = -0.9634757743 Simplifying x = -0.9634757743Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6105345977, -0.9634757743}
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