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Simplifying 10x2 + 88x = 88 Reorder the terms: 88x + 10x2 = 88 Solving 88x + 10x2 = 88 Solving for variable 'x'. Reorder the terms: -88 + 88x + 10x2 = 88 + -88 Combine like terms: 88 + -88 = 0 -88 + 88x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-44 + 44x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-44 + 44x + 5x2)' equal to zero and attempt to solve: Simplifying -44 + 44x + 5x2 = 0 Solving -44 + 44x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -8.8 + 8.8x + x2 = 0 Move the constant term to the right: Add '8.8' to each side of the equation. -8.8 + 8.8x + 8.8 + x2 = 0 + 8.8 Reorder the terms: -8.8 + 8.8 + 8.8x + x2 = 0 + 8.8 Combine like terms: -8.8 + 8.8 = 0.0 0.0 + 8.8x + x2 = 0 + 8.8 8.8x + x2 = 0 + 8.8 Combine like terms: 0 + 8.8 = 8.8 8.8x + x2 = 8.8 The x term is 8.8x. Take half its coefficient (4.4). Square it (19.36) and add it to both sides. Add '19.36' to each side of the equation. 8.8x + 19.36 + x2 = 8.8 + 19.36 Reorder the terms: 19.36 + 8.8x + x2 = 8.8 + 19.36 Combine like terms: 8.8 + 19.36 = 28.16 19.36 + 8.8x + x2 = 28.16 Factor a perfect square on the left side: (x + 4.4)(x + 4.4) = 28.16 Calculate the square root of the right side: 5.306599665 Break this problem into two subproblems by setting (x + 4.4) equal to 5.306599665 and -5.306599665.Subproblem 1
x + 4.4 = 5.306599665 Simplifying x + 4.4 = 5.306599665 Reorder the terms: 4.4 + x = 5.306599665 Solving 4.4 + x = 5.306599665 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.4' to each side of the equation. 4.4 + -4.4 + x = 5.306599665 + -4.4 Combine like terms: 4.4 + -4.4 = 0.0 0.0 + x = 5.306599665 + -4.4 x = 5.306599665 + -4.4 Combine like terms: 5.306599665 + -4.4 = 0.906599665 x = 0.906599665 Simplifying x = 0.906599665Subproblem 2
x + 4.4 = -5.306599665 Simplifying x + 4.4 = -5.306599665 Reorder the terms: 4.4 + x = -5.306599665 Solving 4.4 + x = -5.306599665 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.4' to each side of the equation. 4.4 + -4.4 + x = -5.306599665 + -4.4 Combine like terms: 4.4 + -4.4 = 0.0 0.0 + x = -5.306599665 + -4.4 x = -5.306599665 + -4.4 Combine like terms: -5.306599665 + -4.4 = -9.706599665 x = -9.706599665 Simplifying x = -9.706599665Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.906599665, -9.706599665}Solution
x = {0.906599665, -9.706599665}
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