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Simplifying 2 = -16x2 + 124x Reorder the terms: 2 = 124x + -16x2 Solving 2 = 124x + -16x2 Solving for variable 'x'. Reorder the terms: 2 + -124x + 16x2 = 124x + -124x + -16x2 + 16x2 Combine like terms: 124x + -124x = 0 2 + -124x + 16x2 = 0 + -16x2 + 16x2 2 + -124x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 2 + -124x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(1 + -62x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + -62x + 8x2)' equal to zero and attempt to solve: Simplifying 1 + -62x + 8x2 = 0 Solving 1 + -62x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.125 + -7.75x + x2 = 0 Move the constant term to the right: Add '-0.125' to each side of the equation. 0.125 + -7.75x + -0.125 + x2 = 0 + -0.125 Reorder the terms: 0.125 + -0.125 + -7.75x + x2 = 0 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + -7.75x + x2 = 0 + -0.125 -7.75x + x2 = 0 + -0.125 Combine like terms: 0 + -0.125 = -0.125 -7.75x + x2 = -0.125 The x term is -7.75x. Take half its coefficient (-3.875). Square it (15.015625) and add it to both sides. Add '15.015625' to each side of the equation. -7.75x + 15.015625 + x2 = -0.125 + 15.015625 Reorder the terms: 15.015625 + -7.75x + x2 = -0.125 + 15.015625 Combine like terms: -0.125 + 15.015625 = 14.890625 15.015625 + -7.75x + x2 = 14.890625 Factor a perfect square on the left side: (x + -3.875)(x + -3.875) = 14.890625 Calculate the square root of the right side: 3.85883726 Break this problem into two subproblems by setting (x + -3.875) equal to 3.85883726 and -3.85883726.Subproblem 1
x + -3.875 = 3.85883726 Simplifying x + -3.875 = 3.85883726 Reorder the terms: -3.875 + x = 3.85883726 Solving -3.875 + x = 3.85883726 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.875' to each side of the equation. -3.875 + 3.875 + x = 3.85883726 + 3.875 Combine like terms: -3.875 + 3.875 = 0.000 0.000 + x = 3.85883726 + 3.875 x = 3.85883726 + 3.875 Combine like terms: 3.85883726 + 3.875 = 7.73383726 x = 7.73383726 Simplifying x = 7.73383726Subproblem 2
x + -3.875 = -3.85883726 Simplifying x + -3.875 = -3.85883726 Reorder the terms: -3.875 + x = -3.85883726 Solving -3.875 + x = -3.85883726 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.875' to each side of the equation. -3.875 + 3.875 + x = -3.85883726 + 3.875 Combine like terms: -3.875 + 3.875 = 0.000 0.000 + x = -3.85883726 + 3.875 x = -3.85883726 + 3.875 Combine like terms: -3.85883726 + 3.875 = 0.01616274 x = 0.01616274 Simplifying x = 0.01616274Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.73383726, 0.01616274}Solution
x = {7.73383726, 0.01616274}
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