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Simplifying -16x2 + 128x + 50 = 0 Reorder the terms: 50 + 128x + -16x2 = 0 Solving 50 + 128x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(25 + 64x + -8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(25 + 64x + -8x2)' equal to zero and attempt to solve: Simplifying 25 + 64x + -8x2 = 0 Solving 25 + 64x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -3.125 + -8x + x2 = 0 Move the constant term to the right: Add '3.125' to each side of the equation. -3.125 + -8x + 3.125 + x2 = 0 + 3.125 Reorder the terms: -3.125 + 3.125 + -8x + x2 = 0 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + -8x + x2 = 0 + 3.125 -8x + x2 = 0 + 3.125 Combine like terms: 0 + 3.125 = 3.125 -8x + x2 = 3.125 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 = 3.125 + 16 Reorder the terms: 16 + -8x + x2 = 3.125 + 16 Combine like terms: 3.125 + 16 = 19.125 16 + -8x + x2 = 19.125 Factor a perfect square on the left side: (x + -4)(x + -4) = 19.125 Calculate the square root of the right side: 4.373213921 Break this problem into two subproblems by setting (x + -4) equal to 4.373213921 and -4.373213921.Subproblem 1
x + -4 = 4.373213921 Simplifying x + -4 = 4.373213921 Reorder the terms: -4 + x = 4.373213921 Solving -4 + x = 4.373213921 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 = 4.373213921 + 4 Combine like terms: -4 + 4 = 0 0 + x = 4.373213921 + 4 x = 4.373213921 + 4 Combine like terms: 4.373213921 + 4 = 8.373213921 x = 8.373213921 Simplifying x = 8.373213921Subproblem 2
x + -4 = -4.373213921 Simplifying x + -4 = -4.373213921 Reorder the terms: -4 + x = -4.373213921 Solving -4 + x = -4.373213921 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 = -4.373213921 + 4 Combine like terms: -4 + 4 = 0 0 + x = -4.373213921 + 4 x = -4.373213921 + 4 Combine like terms: -4.373213921 + 4 = -0.373213921 x = -0.373213921 Simplifying x = -0.373213921Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.373213921, -0.373213921}Solution
x = {8.373213921, -0.373213921}
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