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Simplifying 0 = x2 + -9x + -11 Reorder the terms: 0 = -11 + -9x + x2 Solving 0 = -11 + -9x + x2 Solving for variable 'x'. Combine like terms: 0 + 11 = 11 11 + 9x + -1x2 = -11 + -9x + x2 + 11 + 9x + -1x2 Reorder the terms: 11 + 9x + -1x2 = -11 + 11 + -9x + 9x + x2 + -1x2 Combine like terms: -11 + 11 = 0 11 + 9x + -1x2 = 0 + -9x + 9x + x2 + -1x2 11 + 9x + -1x2 = -9x + 9x + x2 + -1x2 Combine like terms: -9x + 9x = 0 11 + 9x + -1x2 = 0 + x2 + -1x2 11 + 9x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 11 + 9x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -11 + -9x + x2 = 0 Move the constant term to the right: Add '11' to each side of the equation. -11 + -9x + 11 + x2 = 0 + 11 Reorder the terms: -11 + 11 + -9x + x2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -9x + x2 = 0 + 11 -9x + x2 = 0 + 11 Combine like terms: 0 + 11 = 11 -9x + x2 = 11 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 = 11 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 11 + 20.25 Combine like terms: 11 + 20.25 = 31.25 20.25 + -9x + x2 = 31.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 31.25 Calculate the square root of the right side: 5.590169944 Break this problem into two subproblems by setting (x + -4.5) equal to 5.590169944 and -5.590169944.Subproblem 1
x + -4.5 = 5.590169944 Simplifying x + -4.5 = 5.590169944 Reorder the terms: -4.5 + x = 5.590169944 Solving -4.5 + x = 5.590169944 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 = 5.590169944 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 5.590169944 + 4.5 x = 5.590169944 + 4.5 Combine like terms: 5.590169944 + 4.5 = 10.090169944 x = 10.090169944 Simplifying x = 10.090169944Subproblem 2
x + -4.5 = -5.590169944 Simplifying x + -4.5 = -5.590169944 Reorder the terms: -4.5 + x = -5.590169944 Solving -4.5 + x = -5.590169944 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 = -5.590169944 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -5.590169944 + 4.5 x = -5.590169944 + 4.5 Combine like terms: -5.590169944 + 4.5 = -1.090169944 x = -1.090169944 Simplifying x = -1.090169944Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.090169944, -1.090169944}
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