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Simplifying 6 + 80x + -16x2 = 0 Solving 6 + 80x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(3 + 40x + -8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + 40x + -8x2)' equal to zero and attempt to solve: Simplifying 3 + 40x + -8x2 = 0 Solving 3 + 40x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -0.375 + -5x + x2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + -5x + 0.375 + x2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + -5x + x2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + -5x + x2 = 0 + 0.375 -5x + x2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 -5x + x2 = 0.375 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 0.375 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 0.375 + 6.25 Combine like terms: 0.375 + 6.25 = 6.625 6.25 + -5x + x2 = 6.625 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 6.625 Calculate the square root of the right side: 2.573907535 Break this problem into two subproblems by setting (x + -2.5) equal to 2.573907535 and -2.573907535.Subproblem 1
x + -2.5 = 2.573907535 Simplifying x + -2.5 = 2.573907535 Reorder the terms: -2.5 + x = 2.573907535 Solving -2.5 + x = 2.573907535 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 2.573907535 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 2.573907535 + 2.5 x = 2.573907535 + 2.5 Combine like terms: 2.573907535 + 2.5 = 5.073907535 x = 5.073907535 Simplifying x = 5.073907535Subproblem 2
x + -2.5 = -2.573907535 Simplifying x + -2.5 = -2.573907535 Reorder the terms: -2.5 + x = -2.573907535 Solving -2.5 + x = -2.573907535 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -2.573907535 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -2.573907535 + 2.5 x = -2.573907535 + 2.5 Combine like terms: -2.573907535 + 2.5 = -0.073907535 x = -0.073907535 Simplifying x = -0.073907535Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.073907535, -0.073907535}Solution
x = {5.073907535, -0.073907535}
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