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Simplifying 110 + (x2 + -5x) = 180 Reorder the terms: 110 + (-5x + x2) = 180 Remove parenthesis around (-5x + x2) 110 + -5x + x2 = 180 Solving 110 + -5x + x2 = 180 Solving for variable 'x'. Reorder the terms: 110 + -180 + -5x + x2 = 180 + -180 Combine like terms: 110 + -180 = -70 -70 + -5x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -70 + -5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '70' to each side of the equation. -70 + -5x + 70 + x2 = 0 + 70 Reorder the terms: -70 + 70 + -5x + x2 = 0 + 70 Combine like terms: -70 + 70 = 0 0 + -5x + x2 = 0 + 70 -5x + x2 = 0 + 70 Combine like terms: 0 + 70 = 70 -5x + x2 = 70 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 = 70 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 70 + 6.25 Combine like terms: 70 + 6.25 = 76.25 6.25 + -5x + x2 = 76.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 76.25 Calculate the square root of the right side: 8.732124598 Break this problem into two subproblems by setting (x + -2.5) equal to 8.732124598 and -8.732124598.Subproblem 1
x + -2.5 = 8.732124598 Simplifying x + -2.5 = 8.732124598 Reorder the terms: -2.5 + x = 8.732124598 Solving -2.5 + x = 8.732124598 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 = 8.732124598 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 8.732124598 + 2.5 x = 8.732124598 + 2.5 Combine like terms: 8.732124598 + 2.5 = 11.232124598 x = 11.232124598 Simplifying x = 11.232124598Subproblem 2
x + -2.5 = -8.732124598 Simplifying x + -2.5 = -8.732124598 Reorder the terms: -2.5 + x = -8.732124598 Solving -2.5 + x = -8.732124598 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 = -8.732124598 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -8.732124598 + 2.5 x = -8.732124598 + 2.5 Combine like terms: -8.732124598 + 2.5 = -6.232124598 x = -6.232124598 Simplifying x = -6.232124598Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.232124598, -6.232124598}
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