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Simplifying 6x2 + -46x + -8 = 0 Reorder the terms: -8 + -46x + 6x2 = 0 Solving -8 + -46x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + -23x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + -23x + 3x2)' equal to zero and attempt to solve: Simplifying -4 + -23x + 3x2 = 0 Solving -4 + -23x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1.333333333 + -7.666666667x + x2 = 0 Move the constant term to the right: Add '1.333333333' to each side of the equation. -1.333333333 + -7.666666667x + 1.333333333 + x2 = 0 + 1.333333333 Reorder the terms: -1.333333333 + 1.333333333 + -7.666666667x + x2 = 0 + 1.333333333 Combine like terms: -1.333333333 + 1.333333333 = 0.000000000 0.000000000 + -7.666666667x + x2 = 0 + 1.333333333 -7.666666667x + x2 = 0 + 1.333333333 Combine like terms: 0 + 1.333333333 = 1.333333333 -7.666666667x + x2 = 1.333333333 The x term is -7.666666667x. Take half its coefficient (-3.833333334). Square it (14.69444445) and add it to both sides. Add '14.69444445' to each side of the equation. -7.666666667x + 14.69444445 + x2 = 1.333333333 + 14.69444445 Reorder the terms: 14.69444445 + -7.666666667x + x2 = 1.333333333 + 14.69444445 Combine like terms: 1.333333333 + 14.69444445 = 16.027777783 14.69444445 + -7.666666667x + x2 = 16.027777783 Factor a perfect square on the left side: (x + -3.833333334)(x + -3.833333334) = 16.027777783 Calculate the square root of the right side: 4.003470717 Break this problem into two subproblems by setting (x + -3.833333334) equal to 4.003470717 and -4.003470717.Subproblem 1
x + -3.833333334 = 4.003470717 Simplifying x + -3.833333334 = 4.003470717 Reorder the terms: -3.833333334 + x = 4.003470717 Solving -3.833333334 + x = 4.003470717 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.833333334' to each side of the equation. -3.833333334 + 3.833333334 + x = 4.003470717 + 3.833333334 Combine like terms: -3.833333334 + 3.833333334 = 0.000000000 0.000000000 + x = 4.003470717 + 3.833333334 x = 4.003470717 + 3.833333334 Combine like terms: 4.003470717 + 3.833333334 = 7.836804051 x = 7.836804051 Simplifying x = 7.836804051Subproblem 2
x + -3.833333334 = -4.003470717 Simplifying x + -3.833333334 = -4.003470717 Reorder the terms: -3.833333334 + x = -4.003470717 Solving -3.833333334 + x = -4.003470717 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.833333334' to each side of the equation. -3.833333334 + 3.833333334 + x = -4.003470717 + 3.833333334 Combine like terms: -3.833333334 + 3.833333334 = 0.000000000 0.000000000 + x = -4.003470717 + 3.833333334 x = -4.003470717 + 3.833333334 Combine like terms: -4.003470717 + 3.833333334 = -0.170137383 x = -0.170137383 Simplifying x = -0.170137383Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.836804051, -0.170137383}Solution
x = {7.836804051, -0.170137383}
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