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Simplifying 0 = -16x2 + 56x + 2 Reorder the terms: 0 = 2 + 56x + -16x2 Solving 0 = 2 + 56x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -2 = -2 -2 + -56x + 16x2 = 2 + 56x + -16x2 + -2 + -56x + 16x2 Reorder the terms: -2 + -56x + 16x2 = 2 + -2 + 56x + -56x + -16x2 + 16x2 Combine like terms: 2 + -2 = 0 -2 + -56x + 16x2 = 0 + 56x + -56x + -16x2 + 16x2 -2 + -56x + 16x2 = 56x + -56x + -16x2 + 16x2 Combine like terms: 56x + -56x = 0 -2 + -56x + 16x2 = 0 + -16x2 + 16x2 -2 + -56x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -2 + -56x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + -28x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -28x + 8x2)' equal to zero and attempt to solve: Simplifying -1 + -28x + 8x2 = 0 Solving -1 + -28x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.125 + -3.5x + x2 = 0 Move the constant term to the right: Add '0.125' to each side of the equation. -0.125 + -3.5x + 0.125 + x2 = 0 + 0.125 Reorder the terms: -0.125 + 0.125 + -3.5x + x2 = 0 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + -3.5x + x2 = 0 + 0.125 -3.5x + x2 = 0 + 0.125 Combine like terms: 0 + 0.125 = 0.125 -3.5x + x2 = 0.125 The x term is -3.5x. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5x + 3.0625 + x2 = 0.125 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = 0.125 + 3.0625 Combine like terms: 0.125 + 3.0625 = 3.1875 3.0625 + -3.5x + x2 = 3.1875 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = 3.1875 Calculate the square root of the right side: 1.785357107 Break this problem into two subproblems by setting (x + -1.75) equal to 1.785357107 and -1.785357107.Subproblem 1
x + -1.75 = 1.785357107 Simplifying x + -1.75 = 1.785357107 Reorder the terms: -1.75 + x = 1.785357107 Solving -1.75 + x = 1.785357107 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = 1.785357107 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 1.785357107 + 1.75 x = 1.785357107 + 1.75 Combine like terms: 1.785357107 + 1.75 = 3.535357107 x = 3.535357107 Simplifying x = 3.535357107Subproblem 2
x + -1.75 = -1.785357107 Simplifying x + -1.75 = -1.785357107 Reorder the terms: -1.75 + x = -1.785357107 Solving -1.75 + x = -1.785357107 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = -1.785357107 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -1.785357107 + 1.75 x = -1.785357107 + 1.75 Combine like terms: -1.785357107 + 1.75 = -0.035357107 x = -0.035357107 Simplifying x = -0.035357107Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.535357107, -0.035357107}Solution
x = {3.535357107, -0.035357107}
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