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Simplifying 0 = x2 + -116x + -2190 Reorder the terms: 0 = -2190 + -116x + x2 Solving 0 = -2190 + -116x + x2 Solving for variable 'x'. Combine like terms: 0 + 2190 = 2190 2190 + 116x + -1x2 = -2190 + -116x + x2 + 2190 + 116x + -1x2 Reorder the terms: 2190 + 116x + -1x2 = -2190 + 2190 + -116x + 116x + x2 + -1x2 Combine like terms: -2190 + 2190 = 0 2190 + 116x + -1x2 = 0 + -116x + 116x + x2 + -1x2 2190 + 116x + -1x2 = -116x + 116x + x2 + -1x2 Combine like terms: -116x + 116x = 0 2190 + 116x + -1x2 = 0 + x2 + -1x2 2190 + 116x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 2190 + 116x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -2190 + -116x + x2 = 0 Move the constant term to the right: Add '2190' to each side of the equation. -2190 + -116x + 2190 + x2 = 0 + 2190 Reorder the terms: -2190 + 2190 + -116x + x2 = 0 + 2190 Combine like terms: -2190 + 2190 = 0 0 + -116x + x2 = 0 + 2190 -116x + x2 = 0 + 2190 Combine like terms: 0 + 2190 = 2190 -116x + x2 = 2190 The x term is -116x. Take half its coefficient (-58). Square it (3364) and add it to both sides. Add '3364' to each side of the equation. -116x + 3364 + x2 = 2190 + 3364 Reorder the terms: 3364 + -116x + x2 = 2190 + 3364 Combine like terms: 2190 + 3364 = 5554 3364 + -116x + x2 = 5554 Factor a perfect square on the left side: (x + -58)(x + -58) = 5554 Calculate the square root of the right side: 74.525163536 Break this problem into two subproblems by setting (x + -58) equal to 74.525163536 and -74.525163536.Subproblem 1
x + -58 = 74.525163536 Simplifying x + -58 = 74.525163536 Reorder the terms: -58 + x = 74.525163536 Solving -58 + x = 74.525163536 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '58' to each side of the equation. -58 + 58 + x = 74.525163536 + 58 Combine like terms: -58 + 58 = 0 0 + x = 74.525163536 + 58 x = 74.525163536 + 58 Combine like terms: 74.525163536 + 58 = 132.525163536 x = 132.525163536 Simplifying x = 132.525163536Subproblem 2
x + -58 = -74.525163536 Simplifying x + -58 = -74.525163536 Reorder the terms: -58 + x = -74.525163536 Solving -58 + x = -74.525163536 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '58' to each side of the equation. -58 + 58 + x = -74.525163536 + 58 Combine like terms: -58 + 58 = 0 0 + x = -74.525163536 + 58 x = -74.525163536 + 58 Combine like terms: -74.525163536 + 58 = -16.525163536 x = -16.525163536 Simplifying x = -16.525163536Solution
The solution to the problem is based on the solutions from the subproblems. x = {132.525163536, -16.525163536}
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