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Simplifying x(8x + 8) = 3x2 + -10 + 35 Reorder the terms: x(8 + 8x) = 3x2 + -10 + 35 (8 * x + 8x * x) = 3x2 + -10 + 35 (8x + 8x2) = 3x2 + -10 + 35 Reorder the terms: 8x + 8x2 = -10 + 35 + 3x2 Combine like terms: -10 + 35 = 25 8x + 8x2 = 25 + 3x2 Solving 8x + 8x2 = 25 + 3x2 Solving for variable 'x'. Reorder the terms: -25 + 8x + 8x2 + -3x2 = 25 + 3x2 + -25 + -3x2 Combine like terms: 8x2 + -3x2 = 5x2 -25 + 8x + 5x2 = 25 + 3x2 + -25 + -3x2 Reorder the terms: -25 + 8x + 5x2 = 25 + -25 + 3x2 + -3x2 Combine like terms: 25 + -25 = 0 -25 + 8x + 5x2 = 0 + 3x2 + -3x2 -25 + 8x + 5x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -25 + 8x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -5 + 1.6x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + 1.6x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + 1.6x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 1.6x + x2 = 0 + 5 1.6x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 1.6x + x2 = 5 The x term is 1.6x. Take half its coefficient (0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. 1.6x + 0.64 + x2 = 5 + 0.64 Reorder the terms: 0.64 + 1.6x + x2 = 5 + 0.64 Combine like terms: 5 + 0.64 = 5.64 0.64 + 1.6x + x2 = 5.64 Factor a perfect square on the left side: (x + 0.8)(x + 0.8) = 5.64 Calculate the square root of the right side: 2.374868417 Break this problem into two subproblems by setting (x + 0.8) equal to 2.374868417 and -2.374868417.Subproblem 1
x + 0.8 = 2.374868417 Simplifying x + 0.8 = 2.374868417 Reorder the terms: 0.8 + x = 2.374868417 Solving 0.8 + x = 2.374868417 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + x = 2.374868417 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = 2.374868417 + -0.8 x = 2.374868417 + -0.8 Combine like terms: 2.374868417 + -0.8 = 1.574868417 x = 1.574868417 Simplifying x = 1.574868417Subproblem 2
x + 0.8 = -2.374868417 Simplifying x + 0.8 = -2.374868417 Reorder the terms: 0.8 + x = -2.374868417 Solving 0.8 + x = -2.374868417 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + x = -2.374868417 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = -2.374868417 + -0.8 x = -2.374868417 + -0.8 Combine like terms: -2.374868417 + -0.8 = -3.174868417 x = -3.174868417 Simplifying x = -3.174868417Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.574868417, -3.174868417}
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