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Simplifying x2 + -122x + 90 = 0 Reorder the terms: 90 + -122x + x2 = 0 Solving 90 + -122x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-90' to each side of the equation. 90 + -122x + -90 + x2 = 0 + -90 Reorder the terms: 90 + -90 + -122x + x2 = 0 + -90 Combine like terms: 90 + -90 = 0 0 + -122x + x2 = 0 + -90 -122x + x2 = 0 + -90 Combine like terms: 0 + -90 = -90 -122x + x2 = -90 The x term is -122x. Take half its coefficient (-61). Square it (3721) and add it to both sides. Add '3721' to each side of the equation. -122x + 3721 + x2 = -90 + 3721 Reorder the terms: 3721 + -122x + x2 = -90 + 3721 Combine like terms: -90 + 3721 = 3631 3721 + -122x + x2 = 3631 Factor a perfect square on the left side: (x + -61)(x + -61) = 3631 Calculate the square root of the right side: 60.257779581 Break this problem into two subproblems by setting (x + -61) equal to 60.257779581 and -60.257779581.Subproblem 1
x + -61 = 60.257779581 Simplifying x + -61 = 60.257779581 Reorder the terms: -61 + x = 60.257779581 Solving -61 + x = 60.257779581 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '61' to each side of the equation. -61 + 61 + x = 60.257779581 + 61 Combine like terms: -61 + 61 = 0 0 + x = 60.257779581 + 61 x = 60.257779581 + 61 Combine like terms: 60.257779581 + 61 = 121.257779581 x = 121.257779581 Simplifying x = 121.257779581Subproblem 2
x + -61 = -60.257779581 Simplifying x + -61 = -60.257779581 Reorder the terms: -61 + x = -60.257779581 Solving -61 + x = -60.257779581 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '61' to each side of the equation. -61 + 61 + x = -60.257779581 + 61 Combine like terms: -61 + 61 = 0 0 + x = -60.257779581 + 61 x = -60.257779581 + 61 Combine like terms: -60.257779581 + 61 = 0.742220419 x = 0.742220419 Simplifying x = 0.742220419Solution
The solution to the problem is based on the solutions from the subproblems. x = {121.257779581, 0.742220419}
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