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Simplifying -16x2 + 8x + 50 = 0 Reorder the terms: 50 + 8x + -16x2 = 0 Solving 50 + 8x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(25 + 4x + -8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(25 + 4x + -8x2)' equal to zero and attempt to solve: Simplifying 25 + 4x + -8x2 = 0 Solving 25 + 4x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -3.125 + -0.5x + x2 = 0 Move the constant term to the right: Add '3.125' to each side of the equation. -3.125 + -0.5x + 3.125 + x2 = 0 + 3.125 Reorder the terms: -3.125 + 3.125 + -0.5x + x2 = 0 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + -0.5x + x2 = 0 + 3.125 -0.5x + x2 = 0 + 3.125 Combine like terms: 0 + 3.125 = 3.125 -0.5x + x2 = 3.125 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 3.125 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 3.125 + 0.0625 Combine like terms: 3.125 + 0.0625 = 3.1875 0.0625 + -0.5x + x2 = 3.1875 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 3.1875 Calculate the square root of the right side: 1.785357107 Break this problem into two subproblems by setting (x + -0.25) equal to 1.785357107 and -1.785357107.Subproblem 1
x + -0.25 = 1.785357107 Simplifying x + -0.25 = 1.785357107 Reorder the terms: -0.25 + x = 1.785357107 Solving -0.25 + x = 1.785357107 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 1.785357107 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 1.785357107 + 0.25 x = 1.785357107 + 0.25 Combine like terms: 1.785357107 + 0.25 = 2.035357107 x = 2.035357107 Simplifying x = 2.035357107Subproblem 2
x + -0.25 = -1.785357107 Simplifying x + -0.25 = -1.785357107 Reorder the terms: -0.25 + x = -1.785357107 Solving -0.25 + x = -1.785357107 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -1.785357107 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -1.785357107 + 0.25 x = -1.785357107 + 0.25 Combine like terms: -1.785357107 + 0.25 = -1.535357107 x = -1.535357107 Simplifying x = -1.535357107Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.035357107, -1.535357107}Solution
x = {2.035357107, -1.535357107}
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