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Simplifying 160x2 + 20x = 100 Reorder the terms: 20x + 160x2 = 100 Solving 20x + 160x2 = 100 Solving for variable 'x'. Reorder the terms: -100 + 20x + 160x2 = 100 + -100 Combine like terms: 100 + -100 = 0 -100 + 20x + 160x2 = 0 Factor out the Greatest Common Factor (GCF), '20'. 20(-5 + x + 8x2) = 0 Ignore the factor 20.Subproblem 1
Set the factor '(-5 + x + 8x2)' equal to zero and attempt to solve: Simplifying -5 + x + 8x2 = 0 Solving -5 + x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.625 + 0.125x + x2 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + 0.125x + 0.625 + x2 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + 0.125x + x2 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + 0.125x + x2 = 0 + 0.625 0.125x + x2 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 0.125x + x2 = 0.625 The x term is x. 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. 0.125x + 0.25 + x2 = 0.625 + 0.25 Reorder the terms: 0.25 + 0.125x + x2 = 0.625 + 0.25 Combine like terms: 0.625 + 0.25 = 0.875 0.25 + 0.125x + x2 = 0.875 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.875 Calculate the square root of the right side: 0.935414347 Break this problem into two subproblems by setting (x + 0.5) equal to 0.935414347 and -0.935414347.Subproblem 1
x + 0.5 = 0.935414347 Simplifying x + 0.5 = 0.935414347 Reorder the terms: 0.5 + x = 0.935414347 Solving 0.5 + x = 0.935414347 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 = 0.935414347 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.935414347 + -0.5 x = 0.935414347 + -0.5 Combine like terms: 0.935414347 + -0.5 = 0.435414347 x = 0.435414347 Simplifying x = 0.435414347Subproblem 2
x + 0.5 = -0.935414347 Simplifying x + 0.5 = -0.935414347 Reorder the terms: 0.5 + x = -0.935414347 Solving 0.5 + x = -0.935414347 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 = -0.935414347 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.935414347 + -0.5 x = -0.935414347 + -0.5 Combine like terms: -0.935414347 + -0.5 = -1.435414347 x = -1.435414347 Simplifying x = -1.435414347Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.435414347, -1.435414347}Solution
x = {0.435414347, -1.435414347}
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