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Simplifying (9 + -0.8x)(5 + -0.4x) = 0 Multiply (9 + -0.8x) * (5 + -0.4x) (9(5 + -0.4x) + -0.8x * (5 + -0.4x)) = 0 ((5 * 9 + -0.4x * 9) + -0.8x * (5 + -0.4x)) = 0 ((45 + -3.6x) + -0.8x * (5 + -0.4x)) = 0 (45 + -3.6x + (5 * -0.8x + -0.4x * -0.8x)) = 0 (45 + -3.6x + (-4x + 0.32x2)) = 0 Combine like terms: -3.6x + -4x = -7.6x (45 + -7.6x + 0.32x2) = 0 Solving 45 + -7.6x + 0.32x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.32 the coefficient of the squared term: Divide each side by '0.32'. 140.625 + -23.75x + x2 = 0 Move the constant term to the right: Add '-140.625' to each side of the equation. 140.625 + -23.75x + -140.625 + x2 = 0 + -140.625 Reorder the terms: 140.625 + -140.625 + -23.75x + x2 = 0 + -140.625 Combine like terms: 140.625 + -140.625 = 0.000 0.000 + -23.75x + x2 = 0 + -140.625 -23.75x + x2 = 0 + -140.625 Combine like terms: 0 + -140.625 = -140.625 -23.75x + x2 = -140.625 The x term is -23.75x. Take half its coefficient (-11.875). Square it (141.015625) and add it to both sides. Add '141.015625' to each side of the equation. -23.75x + 141.015625 + x2 = -140.625 + 141.015625 Reorder the terms: 141.015625 + -23.75x + x2 = -140.625 + 141.015625 Combine like terms: -140.625 + 141.015625 = 0.390625 141.015625 + -23.75x + x2 = 0.390625 Factor a perfect square on the left side: (x + -11.875)(x + -11.875) = 0.390625 Calculate the square root of the right side: 0.625 Break this problem into two subproblems by setting (x + -11.875) equal to 0.625 and -0.625.Subproblem 1
x + -11.875 = 0.625 Simplifying x + -11.875 = 0.625 Reorder the terms: -11.875 + x = 0.625 Solving -11.875 + x = 0.625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.875' to each side of the equation. -11.875 + 11.875 + x = 0.625 + 11.875 Combine like terms: -11.875 + 11.875 = 0.000 0.000 + x = 0.625 + 11.875 x = 0.625 + 11.875 Combine like terms: 0.625 + 11.875 = 12.5 x = 12.5 Simplifying x = 12.5Subproblem 2
x + -11.875 = -0.625 Simplifying x + -11.875 = -0.625 Reorder the terms: -11.875 + x = -0.625 Solving -11.875 + x = -0.625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.875' to each side of the equation. -11.875 + 11.875 + x = -0.625 + 11.875 Combine like terms: -11.875 + 11.875 = 0.000 0.000 + x = -0.625 + 11.875 x = -0.625 + 11.875 Combine like terms: -0.625 + 11.875 = 11.25 x = 11.25 Simplifying x = 11.25Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.5, 11.25}
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