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Simplifying x2 + -28x = -25 Reorder the terms: -28x + x2 = -25 Solving -28x + x2 = -25 Solving for variable 'x'. Reorder the terms: 25 + -28x + x2 = -25 + 25 Combine like terms: -25 + 25 = 0 25 + -28x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-25' to each side of the equation. 25 + -28x + -25 + x2 = 0 + -25 Reorder the terms: 25 + -25 + -28x + x2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -28x + x2 = 0 + -25 -28x + x2 = 0 + -25 Combine like terms: 0 + -25 = -25 -28x + x2 = -25 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 = -25 + 196 Reorder the terms: 196 + -28x + x2 = -25 + 196 Combine like terms: -25 + 196 = 171 196 + -28x + x2 = 171 Factor a perfect square on the left side: (x + -14)(x + -14) = 171 Calculate the square root of the right side: 13.076696831 Break this problem into two subproblems by setting (x + -14) equal to 13.076696831 and -13.076696831.Subproblem 1
x + -14 = 13.076696831 Simplifying x + -14 = 13.076696831 Reorder the terms: -14 + x = 13.076696831 Solving -14 + x = 13.076696831 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 = 13.076696831 + 14 Combine like terms: -14 + 14 = 0 0 + x = 13.076696831 + 14 x = 13.076696831 + 14 Combine like terms: 13.076696831 + 14 = 27.076696831 x = 27.076696831 Simplifying x = 27.076696831Subproblem 2
x + -14 = -13.076696831 Simplifying x + -14 = -13.076696831 Reorder the terms: -14 + x = -13.076696831 Solving -14 + x = -13.076696831 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 = -13.076696831 + 14 Combine like terms: -14 + 14 = 0 0 + x = -13.076696831 + 14 x = -13.076696831 + 14 Combine like terms: -13.076696831 + 14 = 0.923303169 x = 0.923303169 Simplifying x = 0.923303169Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.076696831, 0.923303169}
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