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Simplifying 0 = x2 + -28x + 56 Reorder the terms: 0 = 56 + -28x + x2 Solving 0 = 56 + -28x + x2 Solving for variable 'x'. Combine like terms: 0 + -56 = -56 -56 + 28x + -1x2 = 56 + -28x + x2 + -56 + 28x + -1x2 Reorder the terms: -56 + 28x + -1x2 = 56 + -56 + -28x + 28x + x2 + -1x2 Combine like terms: 56 + -56 = 0 -56 + 28x + -1x2 = 0 + -28x + 28x + x2 + -1x2 -56 + 28x + -1x2 = -28x + 28x + x2 + -1x2 Combine like terms: -28x + 28x = 0 -56 + 28x + -1x2 = 0 + x2 + -1x2 -56 + 28x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -56 + 28x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 56 + -28x + x2 = 0 Move the constant term to the right: Add '-56' to each side of the equation. 56 + -28x + -56 + x2 = 0 + -56 Reorder the terms: 56 + -56 + -28x + x2 = 0 + -56 Combine like terms: 56 + -56 = 0 0 + -28x + x2 = 0 + -56 -28x + x2 = 0 + -56 Combine like terms: 0 + -56 = -56 -28x + x2 = -56 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 = -56 + 196 Reorder the terms: 196 + -28x + x2 = -56 + 196 Combine like terms: -56 + 196 = 140 196 + -28x + x2 = 140 Factor a perfect square on the left side: (x + -14)(x + -14) = 140 Calculate the square root of the right side: 11.832159566 Break this problem into two subproblems by setting (x + -14) equal to 11.832159566 and -11.832159566.Subproblem 1
x + -14 = 11.832159566 Simplifying x + -14 = 11.832159566 Reorder the terms: -14 + x = 11.832159566 Solving -14 + x = 11.832159566 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 = 11.832159566 + 14 Combine like terms: -14 + 14 = 0 0 + x = 11.832159566 + 14 x = 11.832159566 + 14 Combine like terms: 11.832159566 + 14 = 25.832159566 x = 25.832159566 Simplifying x = 25.832159566Subproblem 2
x + -14 = -11.832159566 Simplifying x + -14 = -11.832159566 Reorder the terms: -14 + x = -11.832159566 Solving -14 + x = -11.832159566 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 = -11.832159566 + 14 Combine like terms: -14 + 14 = 0 0 + x = -11.832159566 + 14 x = -11.832159566 + 14 Combine like terms: -11.832159566 + 14 = 2.167840434 x = 2.167840434 Simplifying x = 2.167840434Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.832159566, 2.167840434}
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