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Simplifying -5x + 8x2 + -10x + 5 = 0 Reorder the terms: 5 + -5x + -10x + 8x2 = 0 Combine like terms: -5x + -10x = -15x 5 + -15x + 8x2 = 0 Solving 5 + -15x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.625 + -1.875x + x2 = 0 Move the constant term to the right: Add '-0.625' to each side of the equation. 0.625 + -1.875x + -0.625 + x2 = 0 + -0.625 Reorder the terms: 0.625 + -0.625 + -1.875x + x2 = 0 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + -1.875x + x2 = 0 + -0.625 -1.875x + x2 = 0 + -0.625 Combine like terms: 0 + -0.625 = -0.625 -1.875x + x2 = -0.625 The x term is -1.875x. Take half its coefficient (-0.9375). Square it (0.87890625) and add it to both sides. Add '0.87890625' to each side of the equation. -1.875x + 0.87890625 + x2 = -0.625 + 0.87890625 Reorder the terms: 0.87890625 + -1.875x + x2 = -0.625 + 0.87890625 Combine like terms: -0.625 + 0.87890625 = 0.25390625 0.87890625 + -1.875x + x2 = 0.25390625 Factor a perfect square on the left side: (x + -0.9375)(x + -0.9375) = 0.25390625 Calculate the square root of the right side: 0.503891109 Break this problem into two subproblems by setting (x + -0.9375) equal to 0.503891109 and -0.503891109.Subproblem 1
x + -0.9375 = 0.503891109 Simplifying x + -0.9375 = 0.503891109 Reorder the terms: -0.9375 + x = 0.503891109 Solving -0.9375 + x = 0.503891109 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9375' to each side of the equation. -0.9375 + 0.9375 + x = 0.503891109 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + x = 0.503891109 + 0.9375 x = 0.503891109 + 0.9375 Combine like terms: 0.503891109 + 0.9375 = 1.441391109 x = 1.441391109 Simplifying x = 1.441391109Subproblem 2
x + -0.9375 = -0.503891109 Simplifying x + -0.9375 = -0.503891109 Reorder the terms: -0.9375 + x = -0.503891109 Solving -0.9375 + x = -0.503891109 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9375' to each side of the equation. -0.9375 + 0.9375 + x = -0.503891109 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + x = -0.503891109 + 0.9375 x = -0.503891109 + 0.9375 Combine like terms: -0.503891109 + 0.9375 = 0.433608891 x = 0.433608891 Simplifying x = 0.433608891Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.441391109, 0.433608891}
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