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Simplifying (8x + -2) * 3x + -18 = (8x + -2) Reorder the terms: (-2 + 8x) * 3x + -18 = (8x + -2) Reorder the terms for easier multiplication: 3x(-2 + 8x) + -18 = (8x + -2) (-2 * 3x + 8x * 3x) + -18 = (8x + -2) (-6x + 24x2) + -18 = (8x + -2) Reorder the terms: -18 + -6x + 24x2 = (8x + -2) Reorder the terms: -18 + -6x + 24x2 = (-2 + 8x) Remove parenthesis around (-2 + 8x) -18 + -6x + 24x2 = -2 + 8x Solving -18 + -6x + 24x2 = -2 + 8x Solving for variable 'x'. Reorder the terms: -18 + 2 + -6x + -8x + 24x2 = -2 + 8x + 2 + -8x Combine like terms: -18 + 2 = -16 -16 + -6x + -8x + 24x2 = -2 + 8x + 2 + -8x Combine like terms: -6x + -8x = -14x -16 + -14x + 24x2 = -2 + 8x + 2 + -8x Reorder the terms: -16 + -14x + 24x2 = -2 + 2 + 8x + -8x Combine like terms: -2 + 2 = 0 -16 + -14x + 24x2 = 0 + 8x + -8x -16 + -14x + 24x2 = 8x + -8x Combine like terms: 8x + -8x = 0 -16 + -14x + 24x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-8 + -7x + 12x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-8 + -7x + 12x2)' equal to zero and attempt to solve: Simplifying -8 + -7x + 12x2 = 0 Solving -8 + -7x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -0.6666666667 + -0.5833333333x + x2 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + -0.5833333333x + 0.6666666667 + x2 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + -0.5833333333x + x2 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + -0.5833333333x + x2 = 0 + 0.6666666667 -0.5833333333x + x2 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 -0.5833333333x + x2 = 0.6666666667 The x term is -0.5833333333x. Take half its coefficient (-0.2916666667). Square it (0.08506944446) and add it to both sides. Add '0.08506944446' to each side of the equation. -0.5833333333x + 0.08506944446 + x2 = 0.6666666667 + 0.08506944446 Reorder the terms: 0.08506944446 + -0.5833333333x + x2 = 0.6666666667 + 0.08506944446 Combine like terms: 0.6666666667 + 0.08506944446 = 0.75173611116 0.08506944446 + -0.5833333333x + x2 = 0.75173611116 Factor a perfect square on the left side: (x + -0.2916666667)(x + -0.2916666667) = 0.75173611116 Calculate the square root of the right side: 0.867027169 Break this problem into two subproblems by setting (x + -0.2916666667) equal to 0.867027169 and -0.867027169.Subproblem 1
x + -0.2916666667 = 0.867027169 Simplifying x + -0.2916666667 = 0.867027169 Reorder the terms: -0.2916666667 + x = 0.867027169 Solving -0.2916666667 + x = 0.867027169 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2916666667' to each side of the equation. -0.2916666667 + 0.2916666667 + x = 0.867027169 + 0.2916666667 Combine like terms: -0.2916666667 + 0.2916666667 = 0.0000000000 0.0000000000 + x = 0.867027169 + 0.2916666667 x = 0.867027169 + 0.2916666667 Combine like terms: 0.867027169 + 0.2916666667 = 1.1586938357 x = 1.1586938357 Simplifying x = 1.1586938357Subproblem 2
x + -0.2916666667 = -0.867027169 Simplifying x + -0.2916666667 = -0.867027169 Reorder the terms: -0.2916666667 + x = -0.867027169 Solving -0.2916666667 + x = -0.867027169 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2916666667' to each side of the equation. -0.2916666667 + 0.2916666667 + x = -0.867027169 + 0.2916666667 Combine like terms: -0.2916666667 + 0.2916666667 = 0.0000000000 0.0000000000 + x = -0.867027169 + 0.2916666667 x = -0.867027169 + 0.2916666667 Combine like terms: -0.867027169 + 0.2916666667 = -0.5753605023 x = -0.5753605023 Simplifying x = -0.5753605023Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1586938357, -0.5753605023}Solution
x = {1.1586938357, -0.5753605023}
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