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Simplifying 6x * 6x + 2x + -8 + -14x * 14x = 0 Reorder the terms for easier multiplication: 6 * 6x * x + 2x + -8 + -14x * 14x = 0 Multiply 6 * 6 36x * x + 2x + -8 + -14x * 14x = 0 Multiply x * x 36x2 + 2x + -8 + -14x * 14x = 0 Reorder the terms for easier multiplication: 36x2 + 2x + -8 + -14 * 14x * x = 0 Multiply -14 * 14 36x2 + 2x + -8 + -196x * x = 0 Multiply x * x 36x2 + 2x + -8 + -196x2 = 0 Reorder the terms: -8 + 2x + 36x2 + -196x2 = 0 Combine like terms: 36x2 + -196x2 = -160x2 -8 + 2x + -160x2 = 0 Solving -8 + 2x + -160x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + x + -80x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + x + -80x2)' equal to zero and attempt to solve: Simplifying -4 + x + -80x2 = 0 Solving -4 + x + -80x2 = 0 Begin completing the square. Divide all terms by -80 the coefficient of the squared term: Divide each side by '-80'. 0.05 + -0.0125x + x2 = 0.0 Move the constant term to the right: Add '-0.05' to each side of the equation. 0.05 + -0.0125x + -0.05 + x2 = 0.0 + -0.05 Reorder the terms: 0.05 + -0.05 + -0.0125x + x2 = 0.0 + -0.05 Combine like terms: 0.05 + -0.05 = 0.00 0.00 + -0.0125x + x2 = 0.0 + -0.05 -0.0125x + x2 = 0.0 + -0.05 Combine like terms: 0.0 + -0.05 = -0.05 -0.0125x + x2 = -0.05 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. -0.0125x + 0.25 + x2 = -0.05 + 0.25 Reorder the terms: 0.25 + -0.0125x + x2 = -0.05 + 0.25 Combine like terms: -0.05 + 0.25 = 0.2 0.25 + -0.0125x + x2 = 0.2 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.2 Calculate the square root of the right side: 0.447213596 Break this problem into two subproblems by setting (x + 0.5) equal to 0.447213596 and -0.447213596.Subproblem 1
x + 0.5 = 0.447213596 Simplifying x + 0.5 = 0.447213596 Reorder the terms: 0.5 + x = 0.447213596 Solving 0.5 + x = 0.447213596 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 = 0.447213596 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.447213596 + -0.5 x = 0.447213596 + -0.5 Combine like terms: 0.447213596 + -0.5 = -0.052786404 x = -0.052786404 Simplifying x = -0.052786404Subproblem 2
x + 0.5 = -0.447213596 Simplifying x + 0.5 = -0.447213596 Reorder the terms: 0.5 + x = -0.447213596 Solving 0.5 + x = -0.447213596 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 = -0.447213596 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.447213596 + -0.5 x = -0.447213596 + -0.5 Combine like terms: -0.447213596 + -0.5 = -0.947213596 x = -0.947213596 Simplifying x = -0.947213596Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.052786404, -0.947213596}Solution
x = {-0.052786404, -0.947213596}
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