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Simplifying -2x2 + 34x + -8 = 0 Reorder the terms: -8 + 34x + -2x2 = 0 Solving -8 + 34x + -2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + 17x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + 17x + -1x2)' equal to zero and attempt to solve: Simplifying -4 + 17x + -1x2 = 0 Solving -4 + 17x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 4 + -17x + x2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -17x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -17x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -17x + x2 = 0 + -4 -17x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -17x + x2 = -4 The x term is -17x. Take half its coefficient (-8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. -17x + 72.25 + x2 = -4 + 72.25 Reorder the terms: 72.25 + -17x + x2 = -4 + 72.25 Combine like terms: -4 + 72.25 = 68.25 72.25 + -17x + x2 = 68.25 Factor a perfect square on the left side: (x + -8.5)(x + -8.5) = 68.25 Calculate the square root of the right side: 8.261355821 Break this problem into two subproblems by setting (x + -8.5) equal to 8.261355821 and -8.261355821.Subproblem 1
x + -8.5 = 8.261355821 Simplifying x + -8.5 = 8.261355821 Reorder the terms: -8.5 + x = 8.261355821 Solving -8.5 + x = 8.261355821 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = 8.261355821 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = 8.261355821 + 8.5 x = 8.261355821 + 8.5 Combine like terms: 8.261355821 + 8.5 = 16.761355821 x = 16.761355821 Simplifying x = 16.761355821Subproblem 2
x + -8.5 = -8.261355821 Simplifying x + -8.5 = -8.261355821 Reorder the terms: -8.5 + x = -8.261355821 Solving -8.5 + x = -8.261355821 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = -8.261355821 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = -8.261355821 + 8.5 x = -8.261355821 + 8.5 Combine like terms: -8.261355821 + 8.5 = 0.238644179 x = 0.238644179 Simplifying x = 0.238644179Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.761355821, 0.238644179}Solution
x = {16.761355821, 0.238644179}
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