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Simplifying -5x2 + -55x + 45 = 0 Reorder the terms: 45 + -55x + -5x2 = 0 Solving 45 + -55x + -5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(9 + -11x + -1x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(9 + -11x + -1x2)' equal to zero and attempt to solve: Simplifying 9 + -11x + -1x2 = 0 Solving 9 + -11x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -9 + 11x + x2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + 11x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + 11x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 11x + x2 = 0 + 9 11x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 11x + x2 = 9 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 = 9 + 30.25 Reorder the terms: 30.25 + 11x + x2 = 9 + 30.25 Combine like terms: 9 + 30.25 = 39.25 30.25 + 11x + x2 = 39.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 39.25 Calculate the square root of the right side: 6.264982043 Break this problem into two subproblems by setting (x + 5.5) equal to 6.264982043 and -6.264982043.Subproblem 1
x + 5.5 = 6.264982043 Simplifying x + 5.5 = 6.264982043 Reorder the terms: 5.5 + x = 6.264982043 Solving 5.5 + x = 6.264982043 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 = 6.264982043 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 6.264982043 + -5.5 x = 6.264982043 + -5.5 Combine like terms: 6.264982043 + -5.5 = 0.764982043 x = 0.764982043 Simplifying x = 0.764982043Subproblem 2
x + 5.5 = -6.264982043 Simplifying x + 5.5 = -6.264982043 Reorder the terms: 5.5 + x = -6.264982043 Solving 5.5 + x = -6.264982043 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 = -6.264982043 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -6.264982043 + -5.5 x = -6.264982043 + -5.5 Combine like terms: -6.264982043 + -5.5 = -11.764982043 x = -11.764982043 Simplifying x = -11.764982043Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.764982043, -11.764982043}Solution
x = {0.764982043, -11.764982043}
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