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Simplifying -16x2 + 64x + 50 = 0 Reorder the terms: 50 + 64x + -16x2 = 0 Solving 50 + 64x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(25 + 32x + -8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(25 + 32x + -8x2)' equal to zero and attempt to solve: Simplifying 25 + 32x + -8x2 = 0 Solving 25 + 32x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -3.125 + -4x + x2 = 0 Move the constant term to the right: Add '3.125' to each side of the equation. -3.125 + -4x + 3.125 + x2 = 0 + 3.125 Reorder the terms: -3.125 + 3.125 + -4x + x2 = 0 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + -4x + x2 = 0 + 3.125 -4x + x2 = 0 + 3.125 Combine like terms: 0 + 3.125 = 3.125 -4x + x2 = 3.125 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 3.125 + 4 Reorder the terms: 4 + -4x + x2 = 3.125 + 4 Combine like terms: 3.125 + 4 = 7.125 4 + -4x + x2 = 7.125 Factor a perfect square on the left side: (x + -2)(x + -2) = 7.125 Calculate the square root of the right side: 2.669269563 Break this problem into two subproblems by setting (x + -2) equal to 2.669269563 and -2.669269563.Subproblem 1
x + -2 = 2.669269563 Simplifying x + -2 = 2.669269563 Reorder the terms: -2 + x = 2.669269563 Solving -2 + x = 2.669269563 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 2.669269563 + 2 Combine like terms: -2 + 2 = 0 0 + x = 2.669269563 + 2 x = 2.669269563 + 2 Combine like terms: 2.669269563 + 2 = 4.669269563 x = 4.669269563 Simplifying x = 4.669269563Subproblem 2
x + -2 = -2.669269563 Simplifying x + -2 = -2.669269563 Reorder the terms: -2 + x = -2.669269563 Solving -2 + x = -2.669269563 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -2.669269563 + 2 Combine like terms: -2 + 2 = 0 0 + x = -2.669269563 + 2 x = -2.669269563 + 2 Combine like terms: -2.669269563 + 2 = -0.669269563 x = -0.669269563 Simplifying x = -0.669269563Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.669269563, -0.669269563}Solution
x = {4.669269563, -0.669269563}
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