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Simplifying 936000x2 + -334000x + -635000 = 0 Reorder the terms: -635000 + -334000x + 936000x2 = 0 Solving -635000 + -334000x + 936000x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '1000'. 1000(-635 + -334x + 936x2) = 0 Ignore the factor 1000.Subproblem 1
Set the factor '(-635 + -334x + 936x2)' equal to zero and attempt to solve: Simplifying -635 + -334x + 936x2 = 0 Solving -635 + -334x + 936x2 = 0 Begin completing the square. Divide all terms by 936 the coefficient of the squared term: Divide each side by '936'. -0.6784188034 + -0.3568376068x + x2 = 0 Move the constant term to the right: Add '0.6784188034' to each side of the equation. -0.6784188034 + -0.3568376068x + 0.6784188034 + x2 = 0 + 0.6784188034 Reorder the terms: -0.6784188034 + 0.6784188034 + -0.3568376068x + x2 = 0 + 0.6784188034 Combine like terms: -0.6784188034 + 0.6784188034 = 0.0000000000 0.0000000000 + -0.3568376068x + x2 = 0 + 0.6784188034 -0.3568376068x + x2 = 0 + 0.6784188034 Combine like terms: 0 + 0.6784188034 = 0.6784188034 -0.3568376068x + x2 = 0.6784188034 The x term is -0.3568376068x. Take half its coefficient (-0.1784188034). Square it (0.03183326941) and add it to both sides. Add '0.03183326941' to each side of the equation. -0.3568376068x + 0.03183326941 + x2 = 0.6784188034 + 0.03183326941 Reorder the terms: 0.03183326941 + -0.3568376068x + x2 = 0.6784188034 + 0.03183326941 Combine like terms: 0.6784188034 + 0.03183326941 = 0.71025207281 0.03183326941 + -0.3568376068x + x2 = 0.71025207281 Factor a perfect square on the left side: (x + -0.1784188034)(x + -0.1784188034) = 0.71025207281 Calculate the square root of the right side: 0.842764542 Break this problem into two subproblems by setting (x + -0.1784188034) equal to 0.842764542 and -0.842764542.Subproblem 1
x + -0.1784188034 = 0.842764542 Simplifying x + -0.1784188034 = 0.842764542 Reorder the terms: -0.1784188034 + x = 0.842764542 Solving -0.1784188034 + x = 0.842764542 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1784188034' to each side of the equation. -0.1784188034 + 0.1784188034 + x = 0.842764542 + 0.1784188034 Combine like terms: -0.1784188034 + 0.1784188034 = 0.0000000000 0.0000000000 + x = 0.842764542 + 0.1784188034 x = 0.842764542 + 0.1784188034 Combine like terms: 0.842764542 + 0.1784188034 = 1.0211833454 x = 1.0211833454 Simplifying x = 1.0211833454Subproblem 2
x + -0.1784188034 = -0.842764542 Simplifying x + -0.1784188034 = -0.842764542 Reorder the terms: -0.1784188034 + x = -0.842764542 Solving -0.1784188034 + x = -0.842764542 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1784188034' to each side of the equation. -0.1784188034 + 0.1784188034 + x = -0.842764542 + 0.1784188034 Combine like terms: -0.1784188034 + 0.1784188034 = 0.0000000000 0.0000000000 + x = -0.842764542 + 0.1784188034 x = -0.842764542 + 0.1784188034 Combine like terms: -0.842764542 + 0.1784188034 = -0.6643457386 x = -0.6643457386 Simplifying x = -0.6643457386Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0211833454, -0.6643457386}Solution
x = {1.0211833454, -0.6643457386}
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