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Simplifying (6x + -8)(6x + -8) = 91 Reorder the terms: (-8 + 6x)(6x + -8) = 91 Reorder the terms: (-8 + 6x)(-8 + 6x) = 91 Multiply (-8 + 6x) * (-8 + 6x) (-8(-8 + 6x) + 6x * (-8 + 6x)) = 91 ((-8 * -8 + 6x * -8) + 6x * (-8 + 6x)) = 91 ((64 + -48x) + 6x * (-8 + 6x)) = 91 (64 + -48x + (-8 * 6x + 6x * 6x)) = 91 (64 + -48x + (-48x + 36x2)) = 91 Combine like terms: -48x + -48x = -96x (64 + -96x + 36x2) = 91 Solving 64 + -96x + 36x2 = 91 Solving for variable 'x'. Reorder the terms: 64 + -91 + -96x + 36x2 = 91 + -91 Combine like terms: 64 + -91 = -27 -27 + -96x + 36x2 = 91 + -91 Combine like terms: 91 + -91 = 0 -27 + -96x + 36x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-9 + -32x + 12x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-9 + -32x + 12x2)' equal to zero and attempt to solve: Simplifying -9 + -32x + 12x2 = 0 Solving -9 + -32x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -0.75 + -2.666666667x + x2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + -2.666666667x + 0.75 + x2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + -2.666666667x + x2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + -2.666666667x + x2 = 0 + 0.75 -2.666666667x + x2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 -2.666666667x + x2 = 0.75 The x term is -2.666666667x. Take half its coefficient (-1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. -2.666666667x + 1.777777780 + x2 = 0.75 + 1.777777780 Reorder the terms: 1.777777780 + -2.666666667x + x2 = 0.75 + 1.777777780 Combine like terms: 0.75 + 1.777777780 = 2.52777778 1.777777780 + -2.666666667x + x2 = 2.52777778 Factor a perfect square on the left side: (x + -1.333333334)(x + -1.333333334) = 2.52777778 Calculate the square root of the right side: 1.58989867 Break this problem into two subproblems by setting (x + -1.333333334) equal to 1.58989867 and -1.58989867.Subproblem 1
x + -1.333333334 = 1.58989867 Simplifying x + -1.333333334 = 1.58989867 Reorder the terms: -1.333333334 + x = 1.58989867 Solving -1.333333334 + x = 1.58989867 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.333333334' to each side of the equation. -1.333333334 + 1.333333334 + x = 1.58989867 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = 1.58989867 + 1.333333334 x = 1.58989867 + 1.333333334 Combine like terms: 1.58989867 + 1.333333334 = 2.923232004 x = 2.923232004 Simplifying x = 2.923232004Subproblem 2
x + -1.333333334 = -1.58989867 Simplifying x + -1.333333334 = -1.58989867 Reorder the terms: -1.333333334 + x = -1.58989867 Solving -1.333333334 + x = -1.58989867 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.333333334' to each side of the equation. -1.333333334 + 1.333333334 + x = -1.58989867 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = -1.58989867 + 1.333333334 x = -1.58989867 + 1.333333334 Combine like terms: -1.58989867 + 1.333333334 = -0.256565336 x = -0.256565336 Simplifying x = -0.256565336Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.923232004, -0.256565336}Solution
x = {2.923232004, -0.256565336}
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