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Simplifying -32x2 + -10x + 8 = 0 Reorder the terms: 8 + -10x + -32x2 = 0 Solving 8 + -10x + -32x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(4 + -5x + -16x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4 + -5x + -16x2)' equal to zero and attempt to solve: Simplifying 4 + -5x + -16x2 = 0 Solving 4 + -5x + -16x2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -0.25 + 0.3125x + x2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + 0.3125x + 0.25 + x2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + 0.3125x + x2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + 0.3125x + x2 = 0 + 0.25 0.3125x + x2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 0.3125x + x2 = 0.25 The x term is 0.3125x. Take half its coefficient (0.15625). Square it (0.0244140625) and add it to both sides. Add '0.0244140625' to each side of the equation. 0.3125x + 0.0244140625 + x2 = 0.25 + 0.0244140625 Reorder the terms: 0.0244140625 + 0.3125x + x2 = 0.25 + 0.0244140625 Combine like terms: 0.25 + 0.0244140625 = 0.2744140625 0.0244140625 + 0.3125x + x2 = 0.2744140625 Factor a perfect square on the left side: (x + 0.15625)(x + 0.15625) = 0.2744140625 Calculate the square root of the right side: 0.523845457 Break this problem into two subproblems by setting (x + 0.15625) equal to 0.523845457 and -0.523845457.Subproblem 1
x + 0.15625 = 0.523845457 Simplifying x + 0.15625 = 0.523845457 Reorder the terms: 0.15625 + x = 0.523845457 Solving 0.15625 + x = 0.523845457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.15625' to each side of the equation. 0.15625 + -0.15625 + x = 0.523845457 + -0.15625 Combine like terms: 0.15625 + -0.15625 = 0.00000 0.00000 + x = 0.523845457 + -0.15625 x = 0.523845457 + -0.15625 Combine like terms: 0.523845457 + -0.15625 = 0.367595457 x = 0.367595457 Simplifying x = 0.367595457Subproblem 2
x + 0.15625 = -0.523845457 Simplifying x + 0.15625 = -0.523845457 Reorder the terms: 0.15625 + x = -0.523845457 Solving 0.15625 + x = -0.523845457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.15625' to each side of the equation. 0.15625 + -0.15625 + x = -0.523845457 + -0.15625 Combine like terms: 0.15625 + -0.15625 = 0.00000 0.00000 + x = -0.523845457 + -0.15625 x = -0.523845457 + -0.15625 Combine like terms: -0.523845457 + -0.15625 = -0.680095457 x = -0.680095457 Simplifying x = -0.680095457Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.367595457, -0.680095457}Solution
x = {0.367595457, -0.680095457}
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