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Simplifying x(x + -5) + 65 = 180 Reorder the terms: x(-5 + x) + 65 = 180 (-5 * x + x * x) + 65 = 180 (-5x + x2) + 65 = 180 Reorder the terms: 65 + -5x + x2 = 180 Solving 65 + -5x + x2 = 180 Solving for variable 'x'. Reorder the terms: 65 + -180 + -5x + x2 = 180 + -180 Combine like terms: 65 + -180 = -115 -115 + -5x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -115 + -5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '115' to each side of the equation. -115 + -5x + 115 + x2 = 0 + 115 Reorder the terms: -115 + 115 + -5x + x2 = 0 + 115 Combine like terms: -115 + 115 = 0 0 + -5x + x2 = 0 + 115 -5x + x2 = 0 + 115 Combine like terms: 0 + 115 = 115 -5x + x2 = 115 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 115 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 115 + 6.25 Combine like terms: 115 + 6.25 = 121.25 6.25 + -5x + x2 = 121.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 121.25 Calculate the square root of the right side: 11.011357773 Break this problem into two subproblems by setting (x + -2.5) equal to 11.011357773 and -11.011357773.Subproblem 1
x + -2.5 = 11.011357773 Simplifying x + -2.5 = 11.011357773 Reorder the terms: -2.5 + x = 11.011357773 Solving -2.5 + x = 11.011357773 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 11.011357773 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 11.011357773 + 2.5 x = 11.011357773 + 2.5 Combine like terms: 11.011357773 + 2.5 = 13.511357773 x = 13.511357773 Simplifying x = 13.511357773Subproblem 2
x + -2.5 = -11.011357773 Simplifying x + -2.5 = -11.011357773 Reorder the terms: -2.5 + x = -11.011357773 Solving -2.5 + x = -11.011357773 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -11.011357773 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -11.011357773 + 2.5 x = -11.011357773 + 2.5 Combine like terms: -11.011357773 + 2.5 = -8.511357773 x = -8.511357773 Simplifying x = -8.511357773Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.511357773, -8.511357773}
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