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Simplifying -2x2 + 16x + -26 = 0 Reorder the terms: -26 + 16x + -2x2 = 0 Solving -26 + 16x + -2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-13 + 8x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-13 + 8x + -1x2)' equal to zero and attempt to solve: Simplifying -13 + 8x + -1x2 = 0 Solving -13 + 8x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 13 + -8x + x2 = 0 Move the constant term to the right: Add '-13' to each side of the equation. 13 + -8x + -13 + x2 = 0 + -13 Reorder the terms: 13 + -13 + -8x + x2 = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -8x + x2 = 0 + -13 -8x + x2 = 0 + -13 Combine like terms: 0 + -13 = -13 -8x + x2 = -13 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = -13 + 16 Reorder the terms: 16 + -8x + x2 = -13 + 16 Combine like terms: -13 + 16 = 3 16 + -8x + x2 = 3 Factor a perfect square on the left side: (x + -4)(x + -4) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (x + -4) equal to 1.732050808 and -1.732050808.Subproblem 1
x + -4 = 1.732050808 Simplifying x + -4 = 1.732050808 Reorder the terms: -4 + x = 1.732050808 Solving -4 + x = 1.732050808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 1.732050808 + 4 Combine like terms: -4 + 4 = 0 0 + x = 1.732050808 + 4 x = 1.732050808 + 4 Combine like terms: 1.732050808 + 4 = 5.732050808 x = 5.732050808 Simplifying x = 5.732050808Subproblem 2
x + -4 = -1.732050808 Simplifying x + -4 = -1.732050808 Reorder the terms: -4 + x = -1.732050808 Solving -4 + x = -1.732050808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -1.732050808 + 4 Combine like terms: -4 + 4 = 0 0 + x = -1.732050808 + 4 x = -1.732050808 + 4 Combine like terms: -1.732050808 + 4 = 2.267949192 x = 2.267949192 Simplifying x = 2.267949192Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.732050808, 2.267949192}Solution
x = {5.732050808, 2.267949192}
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