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Simplifying 35x2 + -175x + 200 = 0 Reorder the terms: 200 + -175x + 35x2 = 0 Solving 200 + -175x + 35x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(40 + -35x + 7x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(40 + -35x + 7x2)' equal to zero and attempt to solve: Simplifying 40 + -35x + 7x2 = 0 Solving 40 + -35x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 5.714285714 + -5x + x2 = 0 Move the constant term to the right: Add '-5.714285714' to each side of the equation. 5.714285714 + -5x + -5.714285714 + x2 = 0 + -5.714285714 Reorder the terms: 5.714285714 + -5.714285714 + -5x + x2 = 0 + -5.714285714 Combine like terms: 5.714285714 + -5.714285714 = 0.000000000 0.000000000 + -5x + x2 = 0 + -5.714285714 -5x + x2 = 0 + -5.714285714 Combine like terms: 0 + -5.714285714 = -5.714285714 -5x + x2 = -5.714285714 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = -5.714285714 + 6.25 Reorder the terms: 6.25 + -5x + x2 = -5.714285714 + 6.25 Combine like terms: -5.714285714 + 6.25 = 0.535714286 6.25 + -5x + x2 = 0.535714286 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 0.535714286 Calculate the square root of the right side: 0.731925055 Break this problem into two subproblems by setting (x + -2.5) equal to 0.731925055 and -0.731925055.Subproblem 1
x + -2.5 = 0.731925055 Simplifying x + -2.5 = 0.731925055 Reorder the terms: -2.5 + x = 0.731925055 Solving -2.5 + x = 0.731925055 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 0.731925055 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 0.731925055 + 2.5 x = 0.731925055 + 2.5 Combine like terms: 0.731925055 + 2.5 = 3.231925055 x = 3.231925055 Simplifying x = 3.231925055Subproblem 2
x + -2.5 = -0.731925055 Simplifying x + -2.5 = -0.731925055 Reorder the terms: -2.5 + x = -0.731925055 Solving -2.5 + x = -0.731925055 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -0.731925055 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -0.731925055 + 2.5 x = -0.731925055 + 2.5 Combine like terms: -0.731925055 + 2.5 = 1.768074945 x = 1.768074945 Simplifying x = 1.768074945Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.231925055, 1.768074945}Solution
x = {3.231925055, 1.768074945}
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