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Simplifying 4x + 12x(4x + 6) = 56 Reorder the terms: 4x + 12x(6 + 4x) = 56 4x + (6 * 12x + 4x * 12x) = 56 4x + (72x + 48x2) = 56 Combine like terms: 4x + 72x = 76x 76x + 48x2 = 56 Solving 76x + 48x2 = 56 Solving for variable 'x'. Reorder the terms: -56 + 76x + 48x2 = 56 + -56 Combine like terms: 56 + -56 = 0 -56 + 76x + 48x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-14 + 19x + 12x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-14 + 19x + 12x2)' equal to zero and attempt to solve: Simplifying -14 + 19x + 12x2 = 0 Solving -14 + 19x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -1.166666667 + 1.583333333x + x2 = 0 Move the constant term to the right: Add '1.166666667' to each side of the equation. -1.166666667 + 1.583333333x + 1.166666667 + x2 = 0 + 1.166666667 Reorder the terms: -1.166666667 + 1.166666667 + 1.583333333x + x2 = 0 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + 1.583333333x + x2 = 0 + 1.166666667 1.583333333x + x2 = 0 + 1.166666667 Combine like terms: 0 + 1.166666667 = 1.166666667 1.583333333x + x2 = 1.166666667 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 = 1.166666667 + 0.6267361108 Reorder the terms: 0.6267361108 + 1.583333333x + x2 = 1.166666667 + 0.6267361108 Combine like terms: 1.166666667 + 0.6267361108 = 1.7934027778 0.6267361108 + 1.583333333x + x2 = 1.7934027778 Factor a perfect square on the left side: (x + 0.7916666665)(x + 0.7916666665) = 1.7934027778 Calculate the square root of the right side: 1.33917989 Break this problem into two subproblems by setting (x + 0.7916666665) equal to 1.33917989 and -1.33917989.Subproblem 1
x + 0.7916666665 = 1.33917989 Simplifying x + 0.7916666665 = 1.33917989 Reorder the terms: 0.7916666665 + x = 1.33917989 Solving 0.7916666665 + x = 1.33917989 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 = 1.33917989 + -0.7916666665 Combine like terms: 0.7916666665 + -0.7916666665 = 0.0000000000 0.0000000000 + x = 1.33917989 + -0.7916666665 x = 1.33917989 + -0.7916666665 Combine like terms: 1.33917989 + -0.7916666665 = 0.5475132235 x = 0.5475132235 Simplifying x = 0.5475132235Subproblem 2
x + 0.7916666665 = -1.33917989 Simplifying x + 0.7916666665 = -1.33917989 Reorder the terms: 0.7916666665 + x = -1.33917989 Solving 0.7916666665 + x = -1.33917989 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 = -1.33917989 + -0.7916666665 Combine like terms: 0.7916666665 + -0.7916666665 = 0.0000000000 0.0000000000 + x = -1.33917989 + -0.7916666665 x = -1.33917989 + -0.7916666665 Combine like terms: -1.33917989 + -0.7916666665 = -2.1308465565 x = -2.1308465565 Simplifying x = -2.1308465565Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5475132235, -2.1308465565}Solution
x = {0.5475132235, -2.1308465565}
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