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Simplifying 7056 = x2 + 5x Reorder the terms: 7056 = 5x + x2 Solving 7056 = 5x + x2 Solving for variable 'x'. Reorder the terms: 7056 + -5x + -1x2 = 5x + -5x + x2 + -1x2 Combine like terms: 5x + -5x = 0 7056 + -5x + -1x2 = 0 + x2 + -1x2 7056 + -5x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 7056 + -5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -7056 + 5x + x2 = 0 Move the constant term to the right: Add '7056' to each side of the equation. -7056 + 5x + 7056 + x2 = 0 + 7056 Reorder the terms: -7056 + 7056 + 5x + x2 = 0 + 7056 Combine like terms: -7056 + 7056 = 0 0 + 5x + x2 = 0 + 7056 5x + x2 = 0 + 7056 Combine like terms: 0 + 7056 = 7056 5x + x2 = 7056 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 7056 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 7056 + 6.25 Combine like terms: 7056 + 6.25 = 7062.25 6.25 + 5x + x2 = 7062.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 7062.25 Calculate the square root of the right side: 84.037194146 Break this problem into two subproblems by setting (x + 2.5) equal to 84.037194146 and -84.037194146.Subproblem 1
x + 2.5 = 84.037194146 Simplifying x + 2.5 = 84.037194146 Reorder the terms: 2.5 + x = 84.037194146 Solving 2.5 + x = 84.037194146 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 84.037194146 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 84.037194146 + -2.5 x = 84.037194146 + -2.5 Combine like terms: 84.037194146 + -2.5 = 81.537194146 x = 81.537194146 Simplifying x = 81.537194146Subproblem 2
x + 2.5 = -84.037194146 Simplifying x + 2.5 = -84.037194146 Reorder the terms: 2.5 + x = -84.037194146 Solving 2.5 + x = -84.037194146 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -84.037194146 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -84.037194146 + -2.5 x = -84.037194146 + -2.5 Combine like terms: -84.037194146 + -2.5 = -86.537194146 x = -86.537194146 Simplifying x = -86.537194146Solution
The solution to the problem is based on the solutions from the subproblems. x = {81.537194146, -86.537194146}
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