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Simplifying 313900000 = 20x2 + 20x Reorder the terms: 313900000 = 20x + 20x2 Solving 313900000 = 20x + 20x2 Solving for variable 'x'. Reorder the terms: 313900000 + -20x + -20x2 = 20x + -20x + 20x2 + -20x2 Combine like terms: 20x + -20x = 0 313900000 + -20x + -20x2 = 0 + 20x2 + -20x2 313900000 + -20x + -20x2 = 20x2 + -20x2 Combine like terms: 20x2 + -20x2 = 0 313900000 + -20x + -20x2 = 0 Factor out the Greatest Common Factor (GCF), '20'. 20(15695000 + -1x + -1x2) = 0 Ignore the factor 20.Subproblem 1
Set the factor '(15695000 + -1x + -1x2)' equal to zero and attempt to solve: Simplifying 15695000 + -1x + -1x2 = 0 Solving 15695000 + -1x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -15695000 + x + x2 = 0 Move the constant term to the right: Add '15695000' to each side of the equation. -15695000 + x + 15695000 + x2 = 0 + 15695000 Reorder the terms: -15695000 + 15695000 + x + x2 = 0 + 15695000 Combine like terms: -15695000 + 15695000 = 0 0 + x + x2 = 0 + 15695000 x + x2 = 0 + 15695000 Combine like terms: 0 + 15695000 = 15695000 x + x2 = 15695000 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. + 0.25 + x2 = 15695000 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 15695000 + 0.25 Combine like terms: 15695000 + 0.25 = 15695000.25 1.25 + x2 = 15695000.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 15695000.25 Calculate the square root of the right side: 3961.69158946 Break this problem into two subproblems by setting (x + 0.5) equal to 3961.69158946 and -3961.69158946.Subproblem 1
x + 0.5 = 3961.69158946 Simplifying x + 0.5 = 3961.69158946 Reorder the terms: 0.5 + x = 3961.69158946 Solving 0.5 + x = 3961.69158946 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 = 3961.69158946 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 3961.69158946 + -0.5 x = 3961.69158946 + -0.5 Combine like terms: 3961.69158946 + -0.5 = 3961.19158946 x = 3961.19158946 Simplifying x = 3961.19158946Subproblem 2
x + 0.5 = -3961.69158946 Simplifying x + 0.5 = -3961.69158946 Reorder the terms: 0.5 + x = -3961.69158946 Solving 0.5 + x = -3961.69158946 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 = -3961.69158946 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -3961.69158946 + -0.5 x = -3961.69158946 + -0.5 Combine like terms: -3961.69158946 + -0.5 = -3962.19158946 x = -3962.19158946 Simplifying x = -3962.19158946Solution
The solution to the problem is based on the solutions from the subproblems. x = {3961.19158946, -3962.19158946}Solution
x = {3961.19158946, -3962.19158946}
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