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Simplifying (0.30 + -1x)(0.40 + -1x) = 62.517 Multiply (0.30 + -1x) * (0.40 + -1x) (0.30(0.40 + -1x) + -1x * (0.40 + -1x)) = 62.517 ((0.40 * 0.30 + -1x * 0.30) + -1x * (0.40 + -1x)) = 62.517 ((0.12 + -0.3x) + -1x * (0.40 + -1x)) = 62.517 (0.12 + -0.3x + (0.40 * -1x + -1x * -1x)) = 62.517 (0.12 + -0.3x + (-0.4x + 1x2)) = 62.517 Combine like terms: -0.3x + -0.4x = -0.7x (0.12 + -0.7x + 1x2) = 62.517 Solving 0.12 + -0.7x + 1x2 = 62.517 Solving for variable 'x'. Reorder the terms: 0.12 + -62.517 + -0.7x + 1x2 = 62.517 + -62.517 Combine like terms: 0.12 + -62.517 = -62.397 -62.397 + -0.7x + 1x2 = 62.517 + -62.517 Combine like terms: 62.517 + -62.517 = 0.000 -62.397 + -0.7x + 1x2 = 0.000 Begin completing the square. Move the constant term to the right: Add '62.397' to each side of the equation. -62.397 + -0.7x + 62.397 + x2 = 0.000 + 62.397 Reorder the terms: -62.397 + 62.397 + -0.7x + x2 = 0.000 + 62.397 Combine like terms: -62.397 + 62.397 = 0.000 0.000 + -0.7x + x2 = 0.000 + 62.397 -0.7x + x2 = 0.000 + 62.397 Combine like terms: 0.000 + 62.397 = 62.397 -0.7x + x2 = 62.397 The x term is -0.7x. Take half its coefficient (-0.35). Square it (0.1225) and add it to both sides. Add '0.1225' to each side of the equation. -0.7x + 0.1225 + x2 = 62.397 + 0.1225 Reorder the terms: 0.1225 + -0.7x + x2 = 62.397 + 0.1225 Combine like terms: 62.397 + 0.1225 = 62.5195 0.1225 + -0.7x + x2 = 62.5195 Factor a perfect square on the left side: (x + -0.35)(x + -0.35) = 62.5195 Calculate the square root of the right side: 7.906927343 Break this problem into two subproblems by setting (x + -0.35) equal to 7.906927343 and -7.906927343.Subproblem 1
x + -0.35 = 7.906927343 Simplifying x + -0.35 = 7.906927343 Reorder the terms: -0.35 + x = 7.906927343 Solving -0.35 + x = 7.906927343 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.35' to each side of the equation. -0.35 + 0.35 + x = 7.906927343 + 0.35 Combine like terms: -0.35 + 0.35 = 0.00 0.00 + x = 7.906927343 + 0.35 x = 7.906927343 + 0.35 Combine like terms: 7.906927343 + 0.35 = 8.256927343 x = 8.256927343 Simplifying x = 8.256927343Subproblem 2
x + -0.35 = -7.906927343 Simplifying x + -0.35 = -7.906927343 Reorder the terms: -0.35 + x = -7.906927343 Solving -0.35 + x = -7.906927343 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.35' to each side of the equation. -0.35 + 0.35 + x = -7.906927343 + 0.35 Combine like terms: -0.35 + 0.35 = 0.00 0.00 + x = -7.906927343 + 0.35 x = -7.906927343 + 0.35 Combine like terms: -7.906927343 + 0.35 = -7.556927343 x = -7.556927343 Simplifying x = -7.556927343Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.256927343, -7.556927343}
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