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Simplifying x2 + -5x = 110 Reorder the terms: -5x + x2 = 110 Solving -5x + x2 = 110 Solving for variable 'x'. Reorder the terms: -110 + -5x + x2 = 110 + -110 Combine like terms: 110 + -110 = 0 -110 + -5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '110' to each side of the equation. -110 + -5x + 110 + x2 = 0 + 110 Reorder the terms: -110 + 110 + -5x + x2 = 0 + 110 Combine like terms: -110 + 110 = 0 0 + -5x + x2 = 0 + 110 -5x + x2 = 0 + 110 Combine like terms: 0 + 110 = 110 -5x + x2 = 110 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 = 110 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 110 + 6.25 Combine like terms: 110 + 6.25 = 116.25 6.25 + -5x + x2 = 116.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 116.25 Calculate the square root of the right side: 10.781929326 Break this problem into two subproblems by setting (x + -2.5) equal to 10.781929326 and -10.781929326.Subproblem 1
x + -2.5 = 10.781929326 Simplifying x + -2.5 = 10.781929326 Reorder the terms: -2.5 + x = 10.781929326 Solving -2.5 + x = 10.781929326 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 = 10.781929326 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 10.781929326 + 2.5 x = 10.781929326 + 2.5 Combine like terms: 10.781929326 + 2.5 = 13.281929326 x = 13.281929326 Simplifying x = 13.281929326Subproblem 2
x + -2.5 = -10.781929326 Simplifying x + -2.5 = -10.781929326 Reorder the terms: -2.5 + x = -10.781929326 Solving -2.5 + x = -10.781929326 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 = -10.781929326 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -10.781929326 + 2.5 x = -10.781929326 + 2.5 Combine like terms: -10.781929326 + 2.5 = -8.281929326 x = -8.281929326 Simplifying x = -8.281929326Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.281929326, -8.281929326}
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