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Simplifying x2 + -10x + -81 = -9 Reorder the terms: -81 + -10x + x2 = -9 Solving -81 + -10x + x2 = -9 Solving for variable 'x'. Reorder the terms: -81 + 9 + -10x + x2 = -9 + 9 Combine like terms: -81 + 9 = -72 -72 + -10x + x2 = -9 + 9 Combine like terms: -9 + 9 = 0 -72 + -10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '72' to each side of the equation. -72 + -10x + 72 + x2 = 0 + 72 Reorder the terms: -72 + 72 + -10x + x2 = 0 + 72 Combine like terms: -72 + 72 = 0 0 + -10x + x2 = 0 + 72 -10x + x2 = 0 + 72 Combine like terms: 0 + 72 = 72 -10x + x2 = 72 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = 72 + 25 Reorder the terms: 25 + -10x + x2 = 72 + 25 Combine like terms: 72 + 25 = 97 25 + -10x + x2 = 97 Factor a perfect square on the left side: (x + -5)(x + -5) = 97 Calculate the square root of the right side: 9.848857802 Break this problem into two subproblems by setting (x + -5) equal to 9.848857802 and -9.848857802.Subproblem 1
x + -5 = 9.848857802 Simplifying x + -5 = 9.848857802 Reorder the terms: -5 + x = 9.848857802 Solving -5 + x = 9.848857802 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 9.848857802 + 5 Combine like terms: -5 + 5 = 0 0 + x = 9.848857802 + 5 x = 9.848857802 + 5 Combine like terms: 9.848857802 + 5 = 14.848857802 x = 14.848857802 Simplifying x = 14.848857802Subproblem 2
x + -5 = -9.848857802 Simplifying x + -5 = -9.848857802 Reorder the terms: -5 + x = -9.848857802 Solving -5 + x = -9.848857802 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -9.848857802 + 5 Combine like terms: -5 + 5 = 0 0 + x = -9.848857802 + 5 x = -9.848857802 + 5 Combine like terms: -9.848857802 + 5 = -4.848857802 x = -4.848857802 Simplifying x = -4.848857802Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.848857802, -4.848857802}
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