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Simplifying x2 + -28x + 135 = 0 Reorder the terms: 135 + -28x + x2 = 0 Solving 135 + -28x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-135' to each side of the equation. 135 + -28x + -135 + x2 = 0 + -135 Reorder the terms: 135 + -135 + -28x + x2 = 0 + -135 Combine like terms: 135 + -135 = 0 0 + -28x + x2 = 0 + -135 -28x + x2 = 0 + -135 Combine like terms: 0 + -135 = -135 -28x + x2 = -135 The x term is -28x. Take half its coefficient (-14). Square it (196) and add it to both sides. Add '196' to each side of the equation. -28x + 196 + x2 = -135 + 196 Reorder the terms: 196 + -28x + x2 = -135 + 196 Combine like terms: -135 + 196 = 61 196 + -28x + x2 = 61 Factor a perfect square on the left side: (x + -14)(x + -14) = 61 Calculate the square root of the right side: 7.810249676 Break this problem into two subproblems by setting (x + -14) equal to 7.810249676 and -7.810249676.Subproblem 1
x + -14 = 7.810249676 Simplifying x + -14 = 7.810249676 Reorder the terms: -14 + x = 7.810249676 Solving -14 + x = 7.810249676 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x = 7.810249676 + 14 Combine like terms: -14 + 14 = 0 0 + x = 7.810249676 + 14 x = 7.810249676 + 14 Combine like terms: 7.810249676 + 14 = 21.810249676 x = 21.810249676 Simplifying x = 21.810249676Subproblem 2
x + -14 = -7.810249676 Simplifying x + -14 = -7.810249676 Reorder the terms: -14 + x = -7.810249676 Solving -14 + x = -7.810249676 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x = -7.810249676 + 14 Combine like terms: -14 + 14 = 0 0 + x = -7.810249676 + 14 x = -7.810249676 + 14 Combine like terms: -7.810249676 + 14 = 6.189750324 x = 6.189750324 Simplifying x = 6.189750324Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.810249676, 6.189750324}
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