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Simplifying -80x2 + 2x + 16 = 0 Reorder the terms: 16 + 2x + -80x2 = 0 Solving 16 + 2x + -80x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(8 + x + -40x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(8 + x + -40x2)' equal to zero and attempt to solve: Simplifying 8 + x + -40x2 = 0 Solving 8 + x + -40x2 = 0 Begin completing the square. Divide all terms by -40 the coefficient of the squared term: Divide each side by '-40'. -0.2 + -0.025x + x2 = 0.0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + -0.025x + 0.2 + x2 = 0.0 + 0.2 Reorder the terms: -0.2 + 0.2 + -0.025x + x2 = 0.0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + -0.025x + x2 = 0.0 + 0.2 -0.025x + x2 = 0.0 + 0.2 Combine like terms: 0.0 + 0.2 = 0.2 -0.025x + x2 = 0.2 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -0.025x + 0.25 + x2 = 0.2 + 0.25 Reorder the terms: 0.25 + -0.025x + x2 = 0.2 + 0.25 Combine like terms: 0.2 + 0.25 = 0.45 0.25 + -0.025x + x2 = 0.45 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.45 Calculate the square root of the right side: 0.670820393 Break this problem into two subproblems by setting (x + 0.5) equal to 0.670820393 and -0.670820393.Subproblem 1
x + 0.5 = 0.670820393 Simplifying x + 0.5 = 0.670820393 Reorder the terms: 0.5 + x = 0.670820393 Solving 0.5 + x = 0.670820393 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 0.670820393 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.670820393 + -0.5 x = 0.670820393 + -0.5 Combine like terms: 0.670820393 + -0.5 = 0.170820393 x = 0.170820393 Simplifying x = 0.170820393Subproblem 2
x + 0.5 = -0.670820393 Simplifying x + 0.5 = -0.670820393 Reorder the terms: 0.5 + x = -0.670820393 Solving 0.5 + x = -0.670820393 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -0.670820393 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.670820393 + -0.5 x = -0.670820393 + -0.5 Combine like terms: -0.670820393 + -0.5 = -1.170820393 x = -1.170820393 Simplifying x = -1.170820393Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.170820393, -1.170820393}Solution
x = {0.170820393, -1.170820393}
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