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Simplifying (0.30 + -1x)(0.40 + -1x) = 1.001248 Multiply (0.30 + -1x) * (0.40 + -1x) (0.30(0.40 + -1x) + -1x * (0.40 + -1x)) = 1.001248 ((0.40 * 0.30 + -1x * 0.30) + -1x * (0.40 + -1x)) = 1.001248 ((0.12 + -0.3x) + -1x * (0.40 + -1x)) = 1.001248 (0.12 + -0.3x + (0.40 * -1x + -1x * -1x)) = 1.001248 (0.12 + -0.3x + (-0.4x + 1x2)) = 1.001248 Combine like terms: -0.3x + -0.4x = -0.7x (0.12 + -0.7x + 1x2) = 1.001248 Solving 0.12 + -0.7x + 1x2 = 1.001248 Solving for variable 'x'. Reorder the terms: 0.12 + -1.001248 + -0.7x + 1x2 = 1.001248 + -1.001248 Combine like terms: 0.12 + -1.001248 = -0.881248 -0.881248 + -0.7x + 1x2 = 1.001248 + -1.001248 Combine like terms: 1.001248 + -1.001248 = 0.000000 -0.881248 + -0.7x + 1x2 = 0.000000 Begin completing the square. Move the constant term to the right: Add '0.881248' to each side of the equation. -0.881248 + -0.7x + 0.881248 + x2 = 0.000000 + 0.881248 Reorder the terms: -0.881248 + 0.881248 + -0.7x + x2 = 0.000000 + 0.881248 Combine like terms: -0.881248 + 0.881248 = 0.000000 0.000000 + -0.7x + x2 = 0.000000 + 0.881248 -0.7x + x2 = 0.000000 + 0.881248 Combine like terms: 0.000000 + 0.881248 = 0.881248 -0.7x + x2 = 0.881248 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 = 0.881248 + 0.1225 Reorder the terms: 0.1225 + -0.7x + x2 = 0.881248 + 0.1225 Combine like terms: 0.881248 + 0.1225 = 1.003748 0.1225 + -0.7x + x2 = 1.003748 Factor a perfect square on the left side: (x + -0.35)(x + -0.35) = 1.003748 Calculate the square root of the right side: 1.001872247 Break this problem into two subproblems by setting (x + -0.35) equal to 1.001872247 and -1.001872247.Subproblem 1
x + -0.35 = 1.001872247 Simplifying x + -0.35 = 1.001872247 Reorder the terms: -0.35 + x = 1.001872247 Solving -0.35 + x = 1.001872247 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 = 1.001872247 + 0.35 Combine like terms: -0.35 + 0.35 = 0.00 0.00 + x = 1.001872247 + 0.35 x = 1.001872247 + 0.35 Combine like terms: 1.001872247 + 0.35 = 1.351872247 x = 1.351872247 Simplifying x = 1.351872247Subproblem 2
x + -0.35 = -1.001872247 Simplifying x + -0.35 = -1.001872247 Reorder the terms: -0.35 + x = -1.001872247 Solving -0.35 + x = -1.001872247 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 = -1.001872247 + 0.35 Combine like terms: -0.35 + 0.35 = 0.00 0.00 + x = -1.001872247 + 0.35 x = -1.001872247 + 0.35 Combine like terms: -1.001872247 + 0.35 = -0.651872247 x = -0.651872247 Simplifying x = -0.651872247Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.351872247, -0.651872247}
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