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Simplifying x2 + -2x + -15 = 81 Reorder the terms: -15 + -2x + x2 = 81 Solving -15 + -2x + x2 = 81 Solving for variable 'x'. Reorder the terms: -15 + -81 + -2x + x2 = 81 + -81 Combine like terms: -15 + -81 = -96 -96 + -2x + x2 = 81 + -81 Combine like terms: 81 + -81 = 0 -96 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '96' to each side of the equation. -96 + -2x + 96 + x2 = 0 + 96 Reorder the terms: -96 + 96 + -2x + x2 = 0 + 96 Combine like terms: -96 + 96 = 0 0 + -2x + x2 = 0 + 96 -2x + x2 = 0 + 96 Combine like terms: 0 + 96 = 96 -2x + x2 = 96 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 96 + 1 Reorder the terms: 1 + -2x + x2 = 96 + 1 Combine like terms: 96 + 1 = 97 1 + -2x + x2 = 97 Factor a perfect square on the left side: (x + -1)(x + -1) = 97 Calculate the square root of the right side: 9.848857802 Break this problem into two subproblems by setting (x + -1) equal to 9.848857802 and -9.848857802.Subproblem 1
x + -1 = 9.848857802 Simplifying x + -1 = 9.848857802 Reorder the terms: -1 + x = 9.848857802 Solving -1 + x = 9.848857802 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 9.848857802 + 1 Combine like terms: -1 + 1 = 0 0 + x = 9.848857802 + 1 x = 9.848857802 + 1 Combine like terms: 9.848857802 + 1 = 10.848857802 x = 10.848857802 Simplifying x = 10.848857802Subproblem 2
x + -1 = -9.848857802 Simplifying x + -1 = -9.848857802 Reorder the terms: -1 + x = -9.848857802 Solving -1 + x = -9.848857802 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -9.848857802 + 1 Combine like terms: -1 + 1 = 0 0 + x = -9.848857802 + 1 x = -9.848857802 + 1 Combine like terms: -9.848857802 + 1 = -8.848857802 x = -8.848857802 Simplifying x = -8.848857802Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.848857802, -8.848857802}
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