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Simplifying 144x + 6(3 + -4x) = -4x(8 + -3x) + -6 144x + (3 * 6 + -4x * 6) = -4x(8 + -3x) + -6 144x + (18 + -24x) = -4x(8 + -3x) + -6 Reorder the terms: 18 + 144x + -24x = -4x(8 + -3x) + -6 Combine like terms: 144x + -24x = 120x 18 + 120x = -4x(8 + -3x) + -6 18 + 120x = (8 * -4x + -3x * -4x) + -6 18 + 120x = (-32x + 12x2) + -6 Reorder the terms: 18 + 120x = -6 + -32x + 12x2 Solving 18 + 120x = -6 + -32x + 12x2 Solving for variable 'x'. Reorder the terms: 18 + 6 + 120x + 32x + -12x2 = -6 + -32x + 12x2 + 6 + 32x + -12x2 Combine like terms: 18 + 6 = 24 24 + 120x + 32x + -12x2 = -6 + -32x + 12x2 + 6 + 32x + -12x2 Combine like terms: 120x + 32x = 152x 24 + 152x + -12x2 = -6 + -32x + 12x2 + 6 + 32x + -12x2 Reorder the terms: 24 + 152x + -12x2 = -6 + 6 + -32x + 32x + 12x2 + -12x2 Combine like terms: -6 + 6 = 0 24 + 152x + -12x2 = 0 + -32x + 32x + 12x2 + -12x2 24 + 152x + -12x2 = -32x + 32x + 12x2 + -12x2 Combine like terms: -32x + 32x = 0 24 + 152x + -12x2 = 0 + 12x2 + -12x2 24 + 152x + -12x2 = 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 24 + 152x + -12x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(6 + 38x + -3x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(6 + 38x + -3x2)' equal to zero and attempt to solve: Simplifying 6 + 38x + -3x2 = 0 Solving 6 + 38x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -2 + -12.66666667x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -12.66666667x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -12.66666667x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -12.66666667x + x2 = 0 + 2 -12.66666667x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -12.66666667x + x2 = 2 The x term is -12.66666667x. Take half its coefficient (-6.333333335). Square it (40.11111113) and add it to both sides. Add '40.11111113' to each side of the equation. -12.66666667x + 40.11111113 + x2 = 2 + 40.11111113 Reorder the terms: 40.11111113 + -12.66666667x + x2 = 2 + 40.11111113 Combine like terms: 2 + 40.11111113 = 42.11111113 40.11111113 + -12.66666667x + x2 = 42.11111113 Factor a perfect square on the left side: (x + -6.333333335)(x + -6.333333335) = 42.11111113 Calculate the square root of the right side: 6.489307446 Break this problem into two subproblems by setting (x + -6.333333335) equal to 6.489307446 and -6.489307446.Subproblem 1
x + -6.333333335 = 6.489307446 Simplifying x + -6.333333335 = 6.489307446 Reorder the terms: -6.333333335 + x = 6.489307446 Solving -6.333333335 + x = 6.489307446 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.333333335' to each side of the equation. -6.333333335 + 6.333333335 + x = 6.489307446 + 6.333333335 Combine like terms: -6.333333335 + 6.333333335 = 0.000000000 0.000000000 + x = 6.489307446 + 6.333333335 x = 6.489307446 + 6.333333335 Combine like terms: 6.489307446 + 6.333333335 = 12.822640781 x = 12.822640781 Simplifying x = 12.822640781Subproblem 2
x + -6.333333335 = -6.489307446 Simplifying x + -6.333333335 = -6.489307446 Reorder the terms: -6.333333335 + x = -6.489307446 Solving -6.333333335 + x = -6.489307446 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.333333335' to each side of the equation. -6.333333335 + 6.333333335 + x = -6.489307446 + 6.333333335 Combine like terms: -6.333333335 + 6.333333335 = 0.000000000 0.000000000 + x = -6.489307446 + 6.333333335 x = -6.489307446 + 6.333333335 Combine like terms: -6.489307446 + 6.333333335 = -0.155974111 x = -0.155974111 Simplifying x = -0.155974111Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.822640781, -0.155974111}Solution
x = {12.822640781, -0.155974111}
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