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Simplifying 56x + -2x2 = 8 + 4x Solving 56x + -2x2 = 8 + 4x Solving for variable 'x'. Reorder the terms: -8 + 56x + -4x + -2x2 = 8 + 4x + -8 + -4x Combine like terms: 56x + -4x = 52x -8 + 52x + -2x2 = 8 + 4x + -8 + -4x Reorder the terms: -8 + 52x + -2x2 = 8 + -8 + 4x + -4x Combine like terms: 8 + -8 = 0 -8 + 52x + -2x2 = 0 + 4x + -4x -8 + 52x + -2x2 = 4x + -4x Combine like terms: 4x + -4x = 0 -8 + 52x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + 26x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + 26x + -1x2)' equal to zero and attempt to solve: Simplifying -4 + 26x + -1x2 = 0 Solving -4 + 26x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 4 + -26x + x2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -26x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -26x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -26x + x2 = 0 + -4 -26x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -26x + x2 = -4 The x term is -26x. Take half its coefficient (-13). Square it (169) and add it to both sides. Add '169' to each side of the equation. -26x + 169 + x2 = -4 + 169 Reorder the terms: 169 + -26x + x2 = -4 + 169 Combine like terms: -4 + 169 = 165 169 + -26x + x2 = 165 Factor a perfect square on the left side: (x + -13)(x + -13) = 165 Calculate the square root of the right side: 12.845232579 Break this problem into two subproblems by setting (x + -13) equal to 12.845232579 and -12.845232579.Subproblem 1
x + -13 = 12.845232579 Simplifying x + -13 = 12.845232579 Reorder the terms: -13 + x = 12.845232579 Solving -13 + x = 12.845232579 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x = 12.845232579 + 13 Combine like terms: -13 + 13 = 0 0 + x = 12.845232579 + 13 x = 12.845232579 + 13 Combine like terms: 12.845232579 + 13 = 25.845232579 x = 25.845232579 Simplifying x = 25.845232579Subproblem 2
x + -13 = -12.845232579 Simplifying x + -13 = -12.845232579 Reorder the terms: -13 + x = -12.845232579 Solving -13 + x = -12.845232579 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x = -12.845232579 + 13 Combine like terms: -13 + 13 = 0 0 + x = -12.845232579 + 13 x = -12.845232579 + 13 Combine like terms: -12.845232579 + 13 = 0.154767421 x = 0.154767421 Simplifying x = 0.154767421Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.845232579, 0.154767421}Solution
x = {25.845232579, 0.154767421}
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