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Simplifying 190x + -1x2 + 8625 = 0 Reorder the terms: 8625 + 190x + -1x2 = 0 Solving 8625 + 190x + -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'. -8625 + -190x + x2 = 0 Move the constant term to the right: Add '8625' to each side of the equation. -8625 + -190x + 8625 + x2 = 0 + 8625 Reorder the terms: -8625 + 8625 + -190x + x2 = 0 + 8625 Combine like terms: -8625 + 8625 = 0 0 + -190x + x2 = 0 + 8625 -190x + x2 = 0 + 8625 Combine like terms: 0 + 8625 = 8625 -190x + x2 = 8625 The x term is -190x. Take half its coefficient (-95). Square it (9025) and add it to both sides. Add '9025' to each side of the equation. -190x + 9025 + x2 = 8625 + 9025 Reorder the terms: 9025 + -190x + x2 = 8625 + 9025 Combine like terms: 8625 + 9025 = 17650 9025 + -190x + x2 = 17650 Factor a perfect square on the left side: (x + -95)(x + -95) = 17650 Calculate the square root of the right side: 132.853302556 Break this problem into two subproblems by setting (x + -95) equal to 132.853302556 and -132.853302556.Subproblem 1
x + -95 = 132.853302556 Simplifying x + -95 = 132.853302556 Reorder the terms: -95 + x = 132.853302556 Solving -95 + x = 132.853302556 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '95' to each side of the equation. -95 + 95 + x = 132.853302556 + 95 Combine like terms: -95 + 95 = 0 0 + x = 132.853302556 + 95 x = 132.853302556 + 95 Combine like terms: 132.853302556 + 95 = 227.853302556 x = 227.853302556 Simplifying x = 227.853302556Subproblem 2
x + -95 = -132.853302556 Simplifying x + -95 = -132.853302556 Reorder the terms: -95 + x = -132.853302556 Solving -95 + x = -132.853302556 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '95' to each side of the equation. -95 + 95 + x = -132.853302556 + 95 Combine like terms: -95 + 95 = 0 0 + x = -132.853302556 + 95 x = -132.853302556 + 95 Combine like terms: -132.853302556 + 95 = -37.853302556 x = -37.853302556 Simplifying x = -37.853302556Solution
The solution to the problem is based on the solutions from the subproblems. x = {227.853302556, -37.853302556}
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