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Simplifying 70 = 400x(1 + -1x) 70 = (1 * 400x + -1x * 400x) 70 = (400x + -400x2) Solving 70 = 400x + -400x2 Solving for variable 'x'. Reorder the terms: 70 + -400x + 400x2 = 400x + -400x + -400x2 + 400x2 Combine like terms: 400x + -400x = 0 70 + -400x + 400x2 = 0 + -400x2 + 400x2 70 + -400x + 400x2 = -400x2 + 400x2 Combine like terms: -400x2 + 400x2 = 0 70 + -400x + 400x2 = 0 Factor out the Greatest Common Factor (GCF), '10'. 10(7 + -40x + 40x2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(7 + -40x + 40x2)' equal to zero and attempt to solve: Simplifying 7 + -40x + 40x2 = 0 Solving 7 + -40x + 40x2 = 0 Begin completing the square. Divide all terms by 40 the coefficient of the squared term: Divide each side by '40'. 0.175 + -1x + x2 = 0.0 Move the constant term to the right: Add '-0.175' to each side of the equation. 0.175 + -1x + -0.175 + x2 = 0.0 + -0.175 Reorder the terms: 0.175 + -0.175 + -1x + x2 = 0.0 + -0.175 Combine like terms: 0.175 + -0.175 = 0.000 0.000 + -1x + x2 = 0.0 + -0.175 -1x + x2 = 0.0 + -0.175 Combine like terms: 0.0 + -0.175 = -0.175 -1x + x2 = -0.175 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = -0.175 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -0.175 + 0.25 Combine like terms: -0.175 + 0.25 = 0.075 0.25 + -1x + x2 = 0.075 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 0.075 Calculate the square root of the right side: 0.273861279 Break this problem into two subproblems by setting (x + -0.5) equal to 0.273861279 and -0.273861279.Subproblem 1
x + -0.5 = 0.273861279 Simplifying x + -0.5 = 0.273861279 Reorder the terms: -0.5 + x = 0.273861279 Solving -0.5 + x = 0.273861279 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 0.273861279 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.273861279 + 0.5 x = 0.273861279 + 0.5 Combine like terms: 0.273861279 + 0.5 = 0.773861279 x = 0.773861279 Simplifying x = 0.773861279Subproblem 2
x + -0.5 = -0.273861279 Simplifying x + -0.5 = -0.273861279 Reorder the terms: -0.5 + x = -0.273861279 Solving -0.5 + x = -0.273861279 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -0.273861279 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -0.273861279 + 0.5 x = -0.273861279 + 0.5 Combine like terms: -0.273861279 + 0.5 = 0.226138721 x = 0.226138721 Simplifying x = 0.226138721Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.773861279, 0.226138721}Solution
x = {0.773861279, 0.226138721}
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