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Simplifying 10x2 + 52x + -848 = 0 Reorder the terms: -848 + 52x + 10x2 = 0 Solving -848 + 52x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-424 + 26x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-424 + 26x + 5x2)' equal to zero and attempt to solve: Simplifying -424 + 26x + 5x2 = 0 Solving -424 + 26x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -84.8 + 5.2x + x2 = 0 Move the constant term to the right: Add '84.8' to each side of the equation. -84.8 + 5.2x + 84.8 + x2 = 0 + 84.8 Reorder the terms: -84.8 + 84.8 + 5.2x + x2 = 0 + 84.8 Combine like terms: -84.8 + 84.8 = 0.0 0.0 + 5.2x + x2 = 0 + 84.8 5.2x + x2 = 0 + 84.8 Combine like terms: 0 + 84.8 = 84.8 5.2x + x2 = 84.8 The x term is 5.2x. Take half its coefficient (2.6). Square it (6.76) and add it to both sides. Add '6.76' to each side of the equation. 5.2x + 6.76 + x2 = 84.8 + 6.76 Reorder the terms: 6.76 + 5.2x + x2 = 84.8 + 6.76 Combine like terms: 84.8 + 6.76 = 91.56 6.76 + 5.2x + x2 = 91.56 Factor a perfect square on the left side: (x + 2.6)(x + 2.6) = 91.56 Calculate the square root of the right side: 9.568698971 Break this problem into two subproblems by setting (x + 2.6) equal to 9.568698971 and -9.568698971.Subproblem 1
x + 2.6 = 9.568698971 Simplifying x + 2.6 = 9.568698971 Reorder the terms: 2.6 + x = 9.568698971 Solving 2.6 + x = 9.568698971 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.6' to each side of the equation. 2.6 + -2.6 + x = 9.568698971 + -2.6 Combine like terms: 2.6 + -2.6 = 0.0 0.0 + x = 9.568698971 + -2.6 x = 9.568698971 + -2.6 Combine like terms: 9.568698971 + -2.6 = 6.968698971 x = 6.968698971 Simplifying x = 6.968698971Subproblem 2
x + 2.6 = -9.568698971 Simplifying x + 2.6 = -9.568698971 Reorder the terms: 2.6 + x = -9.568698971 Solving 2.6 + x = -9.568698971 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.6' to each side of the equation. 2.6 + -2.6 + x = -9.568698971 + -2.6 Combine like terms: 2.6 + -2.6 = 0.0 0.0 + x = -9.568698971 + -2.6 x = -9.568698971 + -2.6 Combine like terms: -9.568698971 + -2.6 = -12.168698971 x = -12.168698971 Simplifying x = -12.168698971Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.968698971, -12.168698971}Solution
x = {6.968698971, -12.168698971}
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