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Simplifying 68 = 28x + -1x2 Solving 68 = 28x + -1x2 Solving for variable 'x'. Reorder the terms: 68 + -28x + x2 = 28x + -28x + -1x2 + x2 Combine like terms: 28x + -28x = 0 68 + -28x + x2 = 0 + -1x2 + x2 68 + -28x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 68 + -28x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-68' to each side of the equation. 68 + -28x + -68 + x2 = 0 + -68 Reorder the terms: 68 + -68 + -28x + x2 = 0 + -68 Combine like terms: 68 + -68 = 0 0 + -28x + x2 = 0 + -68 -28x + x2 = 0 + -68 Combine like terms: 0 + -68 = -68 -28x + x2 = -68 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 = -68 + 196 Reorder the terms: 196 + -28x + x2 = -68 + 196 Combine like terms: -68 + 196 = 128 196 + -28x + x2 = 128 Factor a perfect square on the left side: (x + -14)(x + -14) = 128 Calculate the square root of the right side: 11.313708499 Break this problem into two subproblems by setting (x + -14) equal to 11.313708499 and -11.313708499.Subproblem 1
x + -14 = 11.313708499 Simplifying x + -14 = 11.313708499 Reorder the terms: -14 + x = 11.313708499 Solving -14 + x = 11.313708499 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 = 11.313708499 + 14 Combine like terms: -14 + 14 = 0 0 + x = 11.313708499 + 14 x = 11.313708499 + 14 Combine like terms: 11.313708499 + 14 = 25.313708499 x = 25.313708499 Simplifying x = 25.313708499Subproblem 2
x + -14 = -11.313708499 Simplifying x + -14 = -11.313708499 Reorder the terms: -14 + x = -11.313708499 Solving -14 + x = -11.313708499 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 = -11.313708499 + 14 Combine like terms: -14 + 14 = 0 0 + x = -11.313708499 + 14 x = -11.313708499 + 14 Combine like terms: -11.313708499 + 14 = 2.686291501 x = 2.686291501 Simplifying x = 2.686291501Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.313708499, 2.686291501}
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