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Simplifying -6x2 + -1x + -1 = 0 Reorder the terms: -1 + -1x + -6x2 = 0 Solving -1 + -1x + -6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(1 + x + 6x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(1 + x + 6x2)' equal to zero and attempt to solve: Simplifying 1 + x + 6x2 = 0 Solving 1 + x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.1666666667 + 0.1666666667x + x2 = 0 Move the constant term to the right: Add '-0.1666666667' to each side of the equation. 0.1666666667 + 0.1666666667x + -0.1666666667 + x2 = 0 + -0.1666666667 Reorder the terms: 0.1666666667 + -0.1666666667 + 0.1666666667x + x2 = 0 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + 0.1666666667x + x2 = 0 + -0.1666666667 0.1666666667x + x2 = 0 + -0.1666666667 Combine like terms: 0 + -0.1666666667 = -0.1666666667 0.1666666667x + x2 = -0.1666666667 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. 0.1666666667x + 0.25 + x2 = -0.1666666667 + 0.25 Reorder the terms: 0.25 + 0.1666666667x + x2 = -0.1666666667 + 0.25 Combine like terms: -0.1666666667 + 0.25 = 0.0833333333 0.25 + 0.1666666667x + x2 = 0.0833333333 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.0833333333 Calculate the square root of the right side: 0.288675135 Break this problem into two subproblems by setting (x + 0.5) equal to 0.288675135 and -0.288675135.Subproblem 1
x + 0.5 = 0.288675135 Simplifying x + 0.5 = 0.288675135 Reorder the terms: 0.5 + x = 0.288675135 Solving 0.5 + x = 0.288675135 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 = 0.288675135 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.288675135 + -0.5 x = 0.288675135 + -0.5 Combine like terms: 0.288675135 + -0.5 = -0.211324865 x = -0.211324865 Simplifying x = -0.211324865Subproblem 2
x + 0.5 = -0.288675135 Simplifying x + 0.5 = -0.288675135 Reorder the terms: 0.5 + x = -0.288675135 Solving 0.5 + x = -0.288675135 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 = -0.288675135 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.288675135 + -0.5 x = -0.288675135 + -0.5 Combine like terms: -0.288675135 + -0.5 = -0.788675135 x = -0.788675135 Simplifying x = -0.788675135Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.211324865, -0.788675135}Solution
x = {-0.211324865, -0.788675135}
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