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Simplifying 0 = x2 + 53x + -70 Reorder the terms: 0 = -70 + 53x + x2 Solving 0 = -70 + 53x + x2 Solving for variable 'x'. Combine like terms: 0 + 70 = 70 70 + -53x + -1x2 = -70 + 53x + x2 + 70 + -53x + -1x2 Reorder the terms: 70 + -53x + -1x2 = -70 + 70 + 53x + -53x + x2 + -1x2 Combine like terms: -70 + 70 = 0 70 + -53x + -1x2 = 0 + 53x + -53x + x2 + -1x2 70 + -53x + -1x2 = 53x + -53x + x2 + -1x2 Combine like terms: 53x + -53x = 0 70 + -53x + -1x2 = 0 + x2 + -1x2 70 + -53x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 70 + -53x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -70 + 53x + x2 = 0 Move the constant term to the right: Add '70' to each side of the equation. -70 + 53x + 70 + x2 = 0 + 70 Reorder the terms: -70 + 70 + 53x + x2 = 0 + 70 Combine like terms: -70 + 70 = 0 0 + 53x + x2 = 0 + 70 53x + x2 = 0 + 70 Combine like terms: 0 + 70 = 70 53x + x2 = 70 The x term is 53x. Take half its coefficient (26.5). Square it (702.25) and add it to both sides. Add '702.25' to each side of the equation. 53x + 702.25 + x2 = 70 + 702.25 Reorder the terms: 702.25 + 53x + x2 = 70 + 702.25 Combine like terms: 70 + 702.25 = 772.25 702.25 + 53x + x2 = 772.25 Factor a perfect square on the left side: (x + 26.5)(x + 26.5) = 772.25 Calculate the square root of the right side: 27.789386463 Break this problem into two subproblems by setting (x + 26.5) equal to 27.789386463 and -27.789386463.Subproblem 1
x + 26.5 = 27.789386463 Simplifying x + 26.5 = 27.789386463 Reorder the terms: 26.5 + x = 27.789386463 Solving 26.5 + x = 27.789386463 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-26.5' to each side of the equation. 26.5 + -26.5 + x = 27.789386463 + -26.5 Combine like terms: 26.5 + -26.5 = 0.0 0.0 + x = 27.789386463 + -26.5 x = 27.789386463 + -26.5 Combine like terms: 27.789386463 + -26.5 = 1.289386463 x = 1.289386463 Simplifying x = 1.289386463Subproblem 2
x + 26.5 = -27.789386463 Simplifying x + 26.5 = -27.789386463 Reorder the terms: 26.5 + x = -27.789386463 Solving 26.5 + x = -27.789386463 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-26.5' to each side of the equation. 26.5 + -26.5 + x = -27.789386463 + -26.5 Combine like terms: 26.5 + -26.5 = 0.0 0.0 + x = -27.789386463 + -26.5 x = -27.789386463 + -26.5 Combine like terms: -27.789386463 + -26.5 = -54.289386463 x = -54.289386463 Simplifying x = -54.289386463Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.289386463, -54.289386463}
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