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Simplifying 2x2 + 16x = -26 Reorder the terms: 16x + 2x2 = -26 Solving 16x + 2x2 = -26 Solving for variable 'x'. Reorder the terms: 26 + 16x + 2x2 = -26 + 26 Combine like terms: -26 + 26 = 0 26 + 16x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(13 + 8x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(13 + 8x + x2)' equal to zero and attempt to solve: Simplifying 13 + 8x + x2 = 0 Solving 13 + 8x + x2 = 0 Begin completing the square. 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 = -2.267949192 x = -2.267949192 Simplifying x = -2.267949192Subproblem 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 = -5.732050808 x = -5.732050808 Simplifying x = -5.732050808Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.267949192, -5.732050808}Solution
x = {-2.267949192, -5.732050808}
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