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Simplifying -1x2 + 110x + -1300 = 0 Reorder the terms: -1300 + 110x + -1x2 = 0 Solving -1300 + 110x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 1300 + -110x + x2 = 0 Move the constant term to the right: Add '-1300' to each side of the equation. 1300 + -110x + -1300 + x2 = 0 + -1300 Reorder the terms: 1300 + -1300 + -110x + x2 = 0 + -1300 Combine like terms: 1300 + -1300 = 0 0 + -110x + x2 = 0 + -1300 -110x + x2 = 0 + -1300 Combine like terms: 0 + -1300 = -1300 -110x + x2 = -1300 The x term is -110x. Take half its coefficient (-55). Square it (3025) and add it to both sides. Add '3025' to each side of the equation. -110x + 3025 + x2 = -1300 + 3025 Reorder the terms: 3025 + -110x + x2 = -1300 + 3025 Combine like terms: -1300 + 3025 = 1725 3025 + -110x + x2 = 1725 Factor a perfect square on the left side: (x + -55)(x + -55) = 1725 Calculate the square root of the right side: 41.533119315 Break this problem into two subproblems by setting (x + -55) equal to 41.533119315 and -41.533119315.Subproblem 1
x + -55 = 41.533119315 Simplifying x + -55 = 41.533119315 Reorder the terms: -55 + x = 41.533119315 Solving -55 + x = 41.533119315 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '55' to each side of the equation. -55 + 55 + x = 41.533119315 + 55 Combine like terms: -55 + 55 = 0 0 + x = 41.533119315 + 55 x = 41.533119315 + 55 Combine like terms: 41.533119315 + 55 = 96.533119315 x = 96.533119315 Simplifying x = 96.533119315Subproblem 2
x + -55 = -41.533119315 Simplifying x + -55 = -41.533119315 Reorder the terms: -55 + x = -41.533119315 Solving -55 + x = -41.533119315 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '55' to each side of the equation. -55 + 55 + x = -41.533119315 + 55 Combine like terms: -55 + 55 = 0 0 + x = -41.533119315 + 55 x = -41.533119315 + 55 Combine like terms: -41.533119315 + 55 = 13.466880685 x = 13.466880685 Simplifying x = 13.466880685Solution
The solution to the problem is based on the solutions from the subproblems. x = {96.533119315, 13.466880685}
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