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Simplifying 60 + 0.40x = (12 + -0.1x) * x Reorder the terms for easier multiplication: 60 + 0.40x = x(12 + -0.1x) 60 + 0.40x = (12 * x + -0.1x * x) 60 + 0.40x = (12x + -0.1x2) Solving 60 + 0.40x = 12x + -0.1x2 Solving for variable 'x'. Combine like terms: 0.40x + -12x = -11.6x 60 + -11.6x + 0.1x2 = 12x + -0.1x2 + -12x + 0.1x2 Reorder the terms: 60 + -11.6x + 0.1x2 = 12x + -12x + -0.1x2 + 0.1x2 Combine like terms: 12x + -12x = 0 60 + -11.6x + 0.1x2 = 0 + -0.1x2 + 0.1x2 60 + -11.6x + 0.1x2 = -0.1x2 + 0.1x2 Combine like terms: -0.1x2 + 0.1x2 = 0.0 60 + -11.6x + 0.1x2 = 0.0 Begin completing the square. Divide all terms by 0.1 the coefficient of the squared term: Divide each side by '0.1'. 600 + -116x + x2 = 0 Move the constant term to the right: Add '-600' to each side of the equation. 600 + -116x + -600 + x2 = 0 + -600 Reorder the terms: 600 + -600 + -116x + x2 = 0 + -600 Combine like terms: 600 + -600 = 0 0 + -116x + x2 = 0 + -600 -116x + x2 = 0 + -600 Combine like terms: 0 + -600 = -600 -116x + x2 = -600 The x term is -116x. Take half its coefficient (-58). Square it (3364) and add it to both sides. Add '3364' to each side of the equation. -116x + 3364 + x2 = -600 + 3364 Reorder the terms: 3364 + -116x + x2 = -600 + 3364 Combine like terms: -600 + 3364 = 2764 3364 + -116x + x2 = 2764 Factor a perfect square on the left side: (x + -58)(x + -58) = 2764 Calculate the square root of the right side: 52.573757712 Break this problem into two subproblems by setting (x + -58) equal to 52.573757712 and -52.573757712.Subproblem 1
x + -58 = 52.573757712 Simplifying x + -58 = 52.573757712 Reorder the terms: -58 + x = 52.573757712 Solving -58 + x = 52.573757712 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '58' to each side of the equation. -58 + 58 + x = 52.573757712 + 58 Combine like terms: -58 + 58 = 0 0 + x = 52.573757712 + 58 x = 52.573757712 + 58 Combine like terms: 52.573757712 + 58 = 110.573757712 x = 110.573757712 Simplifying x = 110.573757712Subproblem 2
x + -58 = -52.573757712 Simplifying x + -58 = -52.573757712 Reorder the terms: -58 + x = -52.573757712 Solving -58 + x = -52.573757712 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '58' to each side of the equation. -58 + 58 + x = -52.573757712 + 58 Combine like terms: -58 + 58 = 0 0 + x = -52.573757712 + 58 x = -52.573757712 + 58 Combine like terms: -52.573757712 + 58 = 5.426242288 x = 5.426242288 Simplifying x = 5.426242288Solution
The solution to the problem is based on the solutions from the subproblems. x = {110.573757712, 5.426242288}
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