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Simplifying 5.12(x2 + -0.7x + 0.12) = x Reorder the terms: 5.12(0.12 + -0.7x + x2) = x (0.12 * 5.12 + -0.7x * 5.12 + x2 * 5.12) = x (0.6144 + -3.584x + 5.12x2) = x Solving 0.6144 + -3.584x + 5.12x2 = x Solving for variable 'x'. Reorder the terms: 0.6144 + -3.584x + -1x + 5.12x2 = x + -1x Combine like terms: -3.584x + -1x = -4.584x 0.6144 + -4.584x + 5.12x2 = x + -1x Combine like terms: x + -1x = 0 0.6144 + -4.584x + 5.12x2 = 0 Begin completing the square. Divide all terms by 5.12 the coefficient of the squared term: Divide each side by '5.12'. 0.12 + -0.8953125x + x2 = 0 Move the constant term to the right: Add '-0.12' to each side of the equation. 0.12 + -0.8953125x + -0.12 + x2 = 0 + -0.12 Reorder the terms: 0.12 + -0.12 + -0.8953125x + x2 = 0 + -0.12 Combine like terms: 0.12 + -0.12 = 0.00 0.00 + -0.8953125x + x2 = 0 + -0.12 -0.8953125x + x2 = 0 + -0.12 Combine like terms: 0 + -0.12 = -0.12 -0.8953125x + x2 = -0.12 The x term is -0.8953125x. Take half its coefficient (-0.44765625). Square it (0.2003961182) and add it to both sides. Add '0.2003961182' to each side of the equation. -0.8953125x + 0.2003961182 + x2 = -0.12 + 0.2003961182 Reorder the terms: 0.2003961182 + -0.8953125x + x2 = -0.12 + 0.2003961182 Combine like terms: -0.12 + 0.2003961182 = 0.0803961182 0.2003961182 + -0.8953125x + x2 = 0.0803961182 Factor a perfect square on the left side: (x + -0.44765625)(x + -0.44765625) = 0.0803961182 Calculate the square root of the right side: 0.283542092 Break this problem into two subproblems by setting (x + -0.44765625) equal to 0.283542092 and -0.283542092.Subproblem 1
x + -0.44765625 = 0.283542092 Simplifying x + -0.44765625 = 0.283542092 Reorder the terms: -0.44765625 + x = 0.283542092 Solving -0.44765625 + x = 0.283542092 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.44765625' to each side of the equation. -0.44765625 + 0.44765625 + x = 0.283542092 + 0.44765625 Combine like terms: -0.44765625 + 0.44765625 = 0.00000000 0.00000000 + x = 0.283542092 + 0.44765625 x = 0.283542092 + 0.44765625 Combine like terms: 0.283542092 + 0.44765625 = 0.731198342 x = 0.731198342 Simplifying x = 0.731198342Subproblem 2
x + -0.44765625 = -0.283542092 Simplifying x + -0.44765625 = -0.283542092 Reorder the terms: -0.44765625 + x = -0.283542092 Solving -0.44765625 + x = -0.283542092 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.44765625' to each side of the equation. -0.44765625 + 0.44765625 + x = -0.283542092 + 0.44765625 Combine like terms: -0.44765625 + 0.44765625 = 0.00000000 0.00000000 + x = -0.283542092 + 0.44765625 x = -0.283542092 + 0.44765625 Combine like terms: -0.283542092 + 0.44765625 = 0.164114158 x = 0.164114158 Simplifying x = 0.164114158Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.731198342, 0.164114158}
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