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Simplifying 0 = (x2) + -56x + 104 0 = x2 + -56x + 104 Reorder the terms: 0 = 104 + -56x + x2 Solving 0 = 104 + -56x + x2 Solving for variable 'x'. Combine like terms: 0 + -104 = -104 -104 + 56x + -1x2 = 104 + -56x + x2 + -104 + 56x + -1x2 Reorder the terms: -104 + 56x + -1x2 = 104 + -104 + -56x + 56x + x2 + -1x2 Combine like terms: 104 + -104 = 0 -104 + 56x + -1x2 = 0 + -56x + 56x + x2 + -1x2 -104 + 56x + -1x2 = -56x + 56x + x2 + -1x2 Combine like terms: -56x + 56x = 0 -104 + 56x + -1x2 = 0 + x2 + -1x2 -104 + 56x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -104 + 56x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 104 + -56x + x2 = 0 Move the constant term to the right: Add '-104' to each side of the equation. 104 + -56x + -104 + x2 = 0 + -104 Reorder the terms: 104 + -104 + -56x + x2 = 0 + -104 Combine like terms: 104 + -104 = 0 0 + -56x + x2 = 0 + -104 -56x + x2 = 0 + -104 Combine like terms: 0 + -104 = -104 -56x + x2 = -104 The x term is -56x. Take half its coefficient (-28). Square it (784) and add it to both sides. Add '784' to each side of the equation. -56x + 784 + x2 = -104 + 784 Reorder the terms: 784 + -56x + x2 = -104 + 784 Combine like terms: -104 + 784 = 680 784 + -56x + x2 = 680 Factor a perfect square on the left side: (x + -28)(x + -28) = 680 Calculate the square root of the right side: 26.076809621 Break this problem into two subproblems by setting (x + -28) equal to 26.076809621 and -26.076809621.Subproblem 1
x + -28 = 26.076809621 Simplifying x + -28 = 26.076809621 Reorder the terms: -28 + x = 26.076809621 Solving -28 + x = 26.076809621 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '28' to each side of the equation. -28 + 28 + x = 26.076809621 + 28 Combine like terms: -28 + 28 = 0 0 + x = 26.076809621 + 28 x = 26.076809621 + 28 Combine like terms: 26.076809621 + 28 = 54.076809621 x = 54.076809621 Simplifying x = 54.076809621Subproblem 2
x + -28 = -26.076809621 Simplifying x + -28 = -26.076809621 Reorder the terms: -28 + x = -26.076809621 Solving -28 + x = -26.076809621 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '28' to each side of the equation. -28 + 28 + x = -26.076809621 + 28 Combine like terms: -28 + 28 = 0 0 + x = -26.076809621 + 28 x = -26.076809621 + 28 Combine like terms: -26.076809621 + 28 = 1.923190379 x = 1.923190379 Simplifying x = 1.923190379Solution
The solution to the problem is based on the solutions from the subproblems. x = {54.076809621, 1.923190379}
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