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Simplifying x2 + -9x + -91 = 0 Reorder the terms: -91 + -9x + x2 = 0 Solving -91 + -9x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '91' to each side of the equation. -91 + -9x + 91 + x2 = 0 + 91 Reorder the terms: -91 + 91 + -9x + x2 = 0 + 91 Combine like terms: -91 + 91 = 0 0 + -9x + x2 = 0 + 91 -9x + x2 = 0 + 91 Combine like terms: 0 + 91 = 91 -9x + x2 = 91 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = 91 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 91 + 20.25 Combine like terms: 91 + 20.25 = 111.25 20.25 + -9x + x2 = 111.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 111.25 Calculate the square root of the right side: 10.547511555 Break this problem into two subproblems by setting (x + -4.5) equal to 10.547511555 and -10.547511555.Subproblem 1
x + -4.5 = 10.547511555 Simplifying x + -4.5 = 10.547511555 Reorder the terms: -4.5 + x = 10.547511555 Solving -4.5 + x = 10.547511555 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 10.547511555 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 10.547511555 + 4.5 x = 10.547511555 + 4.5 Combine like terms: 10.547511555 + 4.5 = 15.047511555 x = 15.047511555 Simplifying x = 15.047511555Subproblem 2
x + -4.5 = -10.547511555 Simplifying x + -4.5 = -10.547511555 Reorder the terms: -4.5 + x = -10.547511555 Solving -4.5 + x = -10.547511555 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -10.547511555 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -10.547511555 + 4.5 x = -10.547511555 + 4.5 Combine like terms: -10.547511555 + 4.5 = -6.047511555 x = -6.047511555 Simplifying x = -6.047511555Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.047511555, -6.047511555}
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