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Simplifying 7875 = x2 + 29x Reorder the terms: 7875 = 29x + x2 Solving 7875 = 29x + x2 Solving for variable 'x'. Reorder the terms: 7875 + -29x + -1x2 = 29x + -29x + x2 + -1x2 Combine like terms: 29x + -29x = 0 7875 + -29x + -1x2 = 0 + x2 + -1x2 7875 + -29x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 7875 + -29x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -7875 + 29x + x2 = 0 Move the constant term to the right: Add '7875' to each side of the equation. -7875 + 29x + 7875 + x2 = 0 + 7875 Reorder the terms: -7875 + 7875 + 29x + x2 = 0 + 7875 Combine like terms: -7875 + 7875 = 0 0 + 29x + x2 = 0 + 7875 29x + x2 = 0 + 7875 Combine like terms: 0 + 7875 = 7875 29x + x2 = 7875 The x term is 29x. Take half its coefficient (14.5). Square it (210.25) and add it to both sides. Add '210.25' to each side of the equation. 29x + 210.25 + x2 = 7875 + 210.25 Reorder the terms: 210.25 + 29x + x2 = 7875 + 210.25 Combine like terms: 7875 + 210.25 = 8085.25 210.25 + 29x + x2 = 8085.25 Factor a perfect square on the left side: (x + 14.5)(x + 14.5) = 8085.25 Calculate the square root of the right side: 89.918018217 Break this problem into two subproblems by setting (x + 14.5) equal to 89.918018217 and -89.918018217.Subproblem 1
x + 14.5 = 89.918018217 Simplifying x + 14.5 = 89.918018217 Reorder the terms: 14.5 + x = 89.918018217 Solving 14.5 + x = 89.918018217 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14.5' to each side of the equation. 14.5 + -14.5 + x = 89.918018217 + -14.5 Combine like terms: 14.5 + -14.5 = 0.0 0.0 + x = 89.918018217 + -14.5 x = 89.918018217 + -14.5 Combine like terms: 89.918018217 + -14.5 = 75.418018217 x = 75.418018217 Simplifying x = 75.418018217Subproblem 2
x + 14.5 = -89.918018217 Simplifying x + 14.5 = -89.918018217 Reorder the terms: 14.5 + x = -89.918018217 Solving 14.5 + x = -89.918018217 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14.5' to each side of the equation. 14.5 + -14.5 + x = -89.918018217 + -14.5 Combine like terms: 14.5 + -14.5 = 0.0 0.0 + x = -89.918018217 + -14.5 x = -89.918018217 + -14.5 Combine like terms: -89.918018217 + -14.5 = -104.418018217 x = -104.418018217 Simplifying x = -104.418018217Solution
The solution to the problem is based on the solutions from the subproblems. x = {75.418018217, -104.418018217}
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