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Simplifying 0 = x2 + -11x + -90 Reorder the terms: 0 = -90 + -11x + x2 Solving 0 = -90 + -11x + x2 Solving for variable 'x'. Combine like terms: 0 + 90 = 90 90 + 11x + -1x2 = -90 + -11x + x2 + 90 + 11x + -1x2 Reorder the terms: 90 + 11x + -1x2 = -90 + 90 + -11x + 11x + x2 + -1x2 Combine like terms: -90 + 90 = 0 90 + 11x + -1x2 = 0 + -11x + 11x + x2 + -1x2 90 + 11x + -1x2 = -11x + 11x + x2 + -1x2 Combine like terms: -11x + 11x = 0 90 + 11x + -1x2 = 0 + x2 + -1x2 90 + 11x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 90 + 11x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -90 + -11x + x2 = 0 Move the constant term to the right: Add '90' to each side of the equation. -90 + -11x + 90 + x2 = 0 + 90 Reorder the terms: -90 + 90 + -11x + x2 = 0 + 90 Combine like terms: -90 + 90 = 0 0 + -11x + x2 = 0 + 90 -11x + x2 = 0 + 90 Combine like terms: 0 + 90 = 90 -11x + x2 = 90 The x term is -11x. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11x + 30.25 + x2 = 90 + 30.25 Reorder the terms: 30.25 + -11x + x2 = 90 + 30.25 Combine like terms: 90 + 30.25 = 120.25 30.25 + -11x + x2 = 120.25 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 120.25 Calculate the square root of the right side: 10.9658561 Break this problem into two subproblems by setting (x + -5.5) equal to 10.9658561 and -10.9658561.Subproblem 1
x + -5.5 = 10.9658561 Simplifying x + -5.5 = 10.9658561 Reorder the terms: -5.5 + x = 10.9658561 Solving -5.5 + x = 10.9658561 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = 10.9658561 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 10.9658561 + 5.5 x = 10.9658561 + 5.5 Combine like terms: 10.9658561 + 5.5 = 16.4658561 x = 16.4658561 Simplifying x = 16.4658561Subproblem 2
x + -5.5 = -10.9658561 Simplifying x + -5.5 = -10.9658561 Reorder the terms: -5.5 + x = -10.9658561 Solving -5.5 + x = -10.9658561 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = -10.9658561 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -10.9658561 + 5.5 x = -10.9658561 + 5.5 Combine like terms: -10.9658561 + 5.5 = -5.4658561 x = -5.4658561 Simplifying x = -5.4658561Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.4658561, -5.4658561}
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