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Simplifying (5x + -1) + -1(2 + -8x) * x = 0.75 Reorder the terms: (-1 + 5x) + -1(2 + -8x) * x = 0.75 Remove parenthesis around (-1 + 5x) -1 + 5x + -1(2 + -8x) * x = 0.75 Reorder the terms for easier multiplication: -1 + 5x + -1x(2 + -8x) = 0.75 -1 + 5x + (2 * -1x + -8x * -1x) = 0.75 -1 + 5x + (-2x + 8x2) = 0.75 Combine like terms: 5x + -2x = 3x -1 + 3x + 8x2 = 0.75 Solving -1 + 3x + 8x2 = 0.75 Solving for variable 'x'. Reorder the terms: -1 + -0.75 + 3x + 8x2 = 0.75 + -0.75 Combine like terms: -1 + -0.75 = -1.75 -1.75 + 3x + 8x2 = 0.75 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 -1.75 + 3x + 8x2 = 0.00 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.21875 + 0.375x + x2 = 0.00 Move the constant term to the right: Add '0.21875' to each side of the equation. -0.21875 + 0.375x + 0.21875 + x2 = 0.00 + 0.21875 Reorder the terms: -0.21875 + 0.21875 + 0.375x + x2 = 0.00 + 0.21875 Combine like terms: -0.21875 + 0.21875 = 0.00000 0.00000 + 0.375x + x2 = 0.00 + 0.21875 0.375x + x2 = 0.00 + 0.21875 Combine like terms: 0.00 + 0.21875 = 0.21875 0.375x + x2 = 0.21875 The x term is 0.375x. Take half its coefficient (0.1875). Square it (0.03515625) and add it to both sides. Add '0.03515625' to each side of the equation. 0.375x + 0.03515625 + x2 = 0.21875 + 0.03515625 Reorder the terms: 0.03515625 + 0.375x + x2 = 0.21875 + 0.03515625 Combine like terms: 0.21875 + 0.03515625 = 0.25390625 0.03515625 + 0.375x + x2 = 0.25390625 Factor a perfect square on the left side: (x + 0.1875)(x + 0.1875) = 0.25390625 Calculate the square root of the right side: 0.503891109 Break this problem into two subproblems by setting (x + 0.1875) equal to 0.503891109 and -0.503891109.Subproblem 1
x + 0.1875 = 0.503891109 Simplifying x + 0.1875 = 0.503891109 Reorder the terms: 0.1875 + x = 0.503891109 Solving 0.1875 + x = 0.503891109 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1875' to each side of the equation. 0.1875 + -0.1875 + x = 0.503891109 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + x = 0.503891109 + -0.1875 x = 0.503891109 + -0.1875 Combine like terms: 0.503891109 + -0.1875 = 0.316391109 x = 0.316391109 Simplifying x = 0.316391109Subproblem 2
x + 0.1875 = -0.503891109 Simplifying x + 0.1875 = -0.503891109 Reorder the terms: 0.1875 + x = -0.503891109 Solving 0.1875 + x = -0.503891109 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1875' to each side of the equation. 0.1875 + -0.1875 + x = -0.503891109 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + x = -0.503891109 + -0.1875 x = -0.503891109 + -0.1875 Combine like terms: -0.503891109 + -0.1875 = -0.691391109 x = -0.691391109 Simplifying x = -0.691391109Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.316391109, -0.691391109}
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