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Simplifying 0 = x2 + -28x + -64 Reorder the terms: 0 = -64 + -28x + x2 Solving 0 = -64 + -28x + x2 Solving for variable 'x'. Combine like terms: 0 + 64 = 64 64 + 28x + -1x2 = -64 + -28x + x2 + 64 + 28x + -1x2 Reorder the terms: 64 + 28x + -1x2 = -64 + 64 + -28x + 28x + x2 + -1x2 Combine like terms: -64 + 64 = 0 64 + 28x + -1x2 = 0 + -28x + 28x + x2 + -1x2 64 + 28x + -1x2 = -28x + 28x + x2 + -1x2 Combine like terms: -28x + 28x = 0 64 + 28x + -1x2 = 0 + x2 + -1x2 64 + 28x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 64 + 28x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -64 + -28x + x2 = 0 Move the constant term to the right: Add '64' to each side of the equation. -64 + -28x + 64 + x2 = 0 + 64 Reorder the terms: -64 + 64 + -28x + x2 = 0 + 64 Combine like terms: -64 + 64 = 0 0 + -28x + x2 = 0 + 64 -28x + x2 = 0 + 64 Combine like terms: 0 + 64 = 64 -28x + x2 = 64 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 = 64 + 196 Reorder the terms: 196 + -28x + x2 = 64 + 196 Combine like terms: 64 + 196 = 260 196 + -28x + x2 = 260 Factor a perfect square on the left side: (x + -14)(x + -14) = 260 Calculate the square root of the right side: 16.124515497 Break this problem into two subproblems by setting (x + -14) equal to 16.124515497 and -16.124515497.Subproblem 1
x + -14 = 16.124515497 Simplifying x + -14 = 16.124515497 Reorder the terms: -14 + x = 16.124515497 Solving -14 + x = 16.124515497 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 = 16.124515497 + 14 Combine like terms: -14 + 14 = 0 0 + x = 16.124515497 + 14 x = 16.124515497 + 14 Combine like terms: 16.124515497 + 14 = 30.124515497 x = 30.124515497 Simplifying x = 30.124515497Subproblem 2
x + -14 = -16.124515497 Simplifying x + -14 = -16.124515497 Reorder the terms: -14 + x = -16.124515497 Solving -14 + x = -16.124515497 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 = -16.124515497 + 14 Combine like terms: -14 + 14 = 0 0 + x = -16.124515497 + 14 x = -16.124515497 + 14 Combine like terms: -16.124515497 + 14 = -2.124515497 x = -2.124515497 Simplifying x = -2.124515497Solution
The solution to the problem is based on the solutions from the subproblems. x = {30.124515497, -2.124515497}
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