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Simplifying 1036x + -1x2 = 164 Solving 1036x + -1x2 = 164 Solving for variable 'x'. Reorder the terms: -164 + 1036x + -1x2 = 164 + -164 Combine like terms: 164 + -164 = 0 -164 + 1036x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 164 + -1036x + x2 = 0 Move the constant term to the right: Add '-164' to each side of the equation. 164 + -1036x + -164 + x2 = 0 + -164 Reorder the terms: 164 + -164 + -1036x + x2 = 0 + -164 Combine like terms: 164 + -164 = 0 0 + -1036x + x2 = 0 + -164 -1036x + x2 = 0 + -164 Combine like terms: 0 + -164 = -164 -1036x + x2 = -164 The x term is -1036x. Take half its coefficient (-518). Square it (268324) and add it to both sides. Add '268324' to each side of the equation. -1036x + 268324 + x2 = -164 + 268324 Reorder the terms: 268324 + -1036x + x2 = -164 + 268324 Combine like terms: -164 + 268324 = 268160 268324 + -1036x + x2 = 268160 Factor a perfect square on the left side: (x + -518)(x + -518) = 268160 Calculate the square root of the right side: 517.841674646 Break this problem into two subproblems by setting (x + -518) equal to 517.841674646 and -517.841674646.Subproblem 1
x + -518 = 517.841674646 Simplifying x + -518 = 517.841674646 Reorder the terms: -518 + x = 517.841674646 Solving -518 + x = 517.841674646 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '518' to each side of the equation. -518 + 518 + x = 517.841674646 + 518 Combine like terms: -518 + 518 = 0 0 + x = 517.841674646 + 518 x = 517.841674646 + 518 Combine like terms: 517.841674646 + 518 = 1035.841674646 x = 1035.841674646 Simplifying x = 1035.841674646Subproblem 2
x + -518 = -517.841674646 Simplifying x + -518 = -517.841674646 Reorder the terms: -518 + x = -517.841674646 Solving -518 + x = -517.841674646 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '518' to each side of the equation. -518 + 518 + x = -517.841674646 + 518 Combine like terms: -518 + 518 = 0 0 + x = -517.841674646 + 518 x = -517.841674646 + 518 Combine like terms: -517.841674646 + 518 = 0.158325354 x = 0.158325354 Simplifying x = 0.158325354Solution
The solution to the problem is based on the solutions from the subproblems. x = {1035.841674646, 0.158325354}
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