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Simplifying 6x(7 + -4(3 + -1x)) + 4x + -2(6x + -7) = 24 6x(7 + (3 * -4 + -1x * -4)) + 4x + -2(6x + -7) = 24 6x(7 + (-12 + 4x)) + 4x + -2(6x + -7) = 24 Combine like terms: 7 + -12 = -5 6x(-5 + 4x) + 4x + -2(6x + -7) = 24 (-5 * 6x + 4x * 6x) + 4x + -2(6x + -7) = 24 (-30x + 24x2) + 4x + -2(6x + -7) = 24 Reorder the terms: -30x + 24x2 + 4x + -2(-7 + 6x) = 24 -30x + 24x2 + 4x + (-7 * -2 + 6x * -2) = 24 -30x + 24x2 + 4x + (14 + -12x) = 24 Reorder the terms: 14 + -30x + 4x + -12x + 24x2 = 24 Combine like terms: -30x + 4x = -26x 14 + -26x + -12x + 24x2 = 24 Combine like terms: -26x + -12x = -38x 14 + -38x + 24x2 = 24 Solving 14 + -38x + 24x2 = 24 Solving for variable 'x'. Reorder the terms: 14 + -24 + -38x + 24x2 = 24 + -24 Combine like terms: 14 + -24 = -10 -10 + -38x + 24x2 = 24 + -24 Combine like terms: 24 + -24 = 0 -10 + -38x + 24x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + -19x + 12x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + -19x + 12x2)' equal to zero and attempt to solve: Simplifying -5 + -19x + 12x2 = 0 Solving -5 + -19x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -0.4166666667 + -1.583333333x + x2 = 0 Move the constant term to the right: Add '0.4166666667' to each side of the equation. -0.4166666667 + -1.583333333x + 0.4166666667 + x2 = 0 + 0.4166666667 Reorder the terms: -0.4166666667 + 0.4166666667 + -1.583333333x + x2 = 0 + 0.4166666667 Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000 0.0000000000 + -1.583333333x + x2 = 0 + 0.4166666667 -1.583333333x + x2 = 0 + 0.4166666667 Combine like terms: 0 + 0.4166666667 = 0.4166666667 -1.583333333x + x2 = 0.4166666667 The x term is -1.583333333x. Take half its coefficient (-0.7916666665). Square it (0.6267361108) and add it to both sides. Add '0.6267361108' to each side of the equation. -1.583333333x + 0.6267361108 + x2 = 0.4166666667 + 0.6267361108 Reorder the terms: 0.6267361108 + -1.583333333x + x2 = 0.4166666667 + 0.6267361108 Combine like terms: 0.4166666667 + 0.6267361108 = 1.0434027775 0.6267361108 + -1.583333333x + x2 = 1.0434027775 Factor a perfect square on the left side: (x + -0.7916666665)(x + -0.7916666665) = 1.0434027775 Calculate the square root of the right side: 1.021470889 Break this problem into two subproblems by setting (x + -0.7916666665) equal to 1.021470889 and -1.021470889.Subproblem 1
x + -0.7916666665 = 1.021470889 Simplifying x + -0.7916666665 = 1.021470889 Reorder the terms: -0.7916666665 + x = 1.021470889 Solving -0.7916666665 + x = 1.021470889 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7916666665' to each side of the equation. -0.7916666665 + 0.7916666665 + x = 1.021470889 + 0.7916666665 Combine like terms: -0.7916666665 + 0.7916666665 = 0.0000000000 0.0000000000 + x = 1.021470889 + 0.7916666665 x = 1.021470889 + 0.7916666665 Combine like terms: 1.021470889 + 0.7916666665 = 1.8131375555 x = 1.8131375555 Simplifying x = 1.8131375555Subproblem 2
x + -0.7916666665 = -1.021470889 Simplifying x + -0.7916666665 = -1.021470889 Reorder the terms: -0.7916666665 + x = -1.021470889 Solving -0.7916666665 + x = -1.021470889 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7916666665' to each side of the equation. -0.7916666665 + 0.7916666665 + x = -1.021470889 + 0.7916666665 Combine like terms: -0.7916666665 + 0.7916666665 = 0.0000000000 0.0000000000 + x = -1.021470889 + 0.7916666665 x = -1.021470889 + 0.7916666665 Combine like terms: -1.021470889 + 0.7916666665 = -0.2298042225 x = -0.2298042225 Simplifying x = -0.2298042225Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.8131375555, -0.2298042225}Solution
x = {1.8131375555, -0.2298042225}
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