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Simplifying -16x2 + 32x + 10 = 0 Reorder the terms: 10 + 32x + -16x2 = 0 Solving 10 + 32x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(5 + 16x + -8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + 16x + -8x2)' equal to zero and attempt to solve: Simplifying 5 + 16x + -8x2 = 0 Solving 5 + 16x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -0.625 + -2x + x2 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + -2x + 0.625 + x2 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + -2x + x2 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + -2x + x2 = 0 + 0.625 -2x + x2 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 -2x + x2 = 0.625 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 0.625 + 1 Reorder the terms: 1 + -2x + x2 = 0.625 + 1 Combine like terms: 0.625 + 1 = 1.625 1 + -2x + x2 = 1.625 Factor a perfect square on the left side: (x + -1)(x + -1) = 1.625 Calculate the square root of the right side: 1.274754878 Break this problem into two subproblems by setting (x + -1) equal to 1.274754878 and -1.274754878.Subproblem 1
x + -1 = 1.274754878 Simplifying x + -1 = 1.274754878 Reorder the terms: -1 + x = 1.274754878 Solving -1 + x = 1.274754878 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 1.274754878 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.274754878 + 1 x = 1.274754878 + 1 Combine like terms: 1.274754878 + 1 = 2.274754878 x = 2.274754878 Simplifying x = 2.274754878Subproblem 2
x + -1 = -1.274754878 Simplifying x + -1 = -1.274754878 Reorder the terms: -1 + x = -1.274754878 Solving -1 + x = -1.274754878 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -1.274754878 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.274754878 + 1 x = -1.274754878 + 1 Combine like terms: -1.274754878 + 1 = -0.274754878 x = -0.274754878 Simplifying x = -0.274754878Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.274754878, -0.274754878}Solution
x = {2.274754878, -0.274754878}
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