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Simplifying (3x + 2)(6 + -2x) = 4 Reorder the terms: (2 + 3x)(6 + -2x) = 4 Multiply (2 + 3x) * (6 + -2x) (2(6 + -2x) + 3x * (6 + -2x)) = 4 ((6 * 2 + -2x * 2) + 3x * (6 + -2x)) = 4 ((12 + -4x) + 3x * (6 + -2x)) = 4 (12 + -4x + (6 * 3x + -2x * 3x)) = 4 (12 + -4x + (18x + -6x2)) = 4 Combine like terms: -4x + 18x = 14x (12 + 14x + -6x2) = 4 Solving 12 + 14x + -6x2 = 4 Solving for variable 'x'. Reorder the terms: 12 + -4 + 14x + -6x2 = 4 + -4 Combine like terms: 12 + -4 = 8 8 + 14x + -6x2 = 4 + -4 Combine like terms: 4 + -4 = 0 8 + 14x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(4 + 7x + -3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4 + 7x + -3x2)' equal to zero and attempt to solve: Simplifying 4 + 7x + -3x2 = 0 Solving 4 + 7x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -1.333333333 + -2.333333333x + x2 = 0 Move the constant term to the right: Add '1.333333333' to each side of the equation. -1.333333333 + -2.333333333x + 1.333333333 + x2 = 0 + 1.333333333 Reorder the terms: -1.333333333 + 1.333333333 + -2.333333333x + x2 = 0 + 1.333333333 Combine like terms: -1.333333333 + 1.333333333 = 0.000000000 0.000000000 + -2.333333333x + x2 = 0 + 1.333333333 -2.333333333x + x2 = 0 + 1.333333333 Combine like terms: 0 + 1.333333333 = 1.333333333 -2.333333333x + x2 = 1.333333333 The x term is -2.333333333x. Take half its coefficient (-1.166666667). Square it (1.361111112) and add it to both sides. Add '1.361111112' to each side of the equation. -2.333333333x + 1.361111112 + x2 = 1.333333333 + 1.361111112 Reorder the terms: 1.361111112 + -2.333333333x + x2 = 1.333333333 + 1.361111112 Combine like terms: 1.333333333 + 1.361111112 = 2.694444445 1.361111112 + -2.333333333x + x2 = 2.694444445 Factor a perfect square on the left side: (x + -1.166666667)(x + -1.166666667) = 2.694444445 Calculate the square root of the right side: 1.6414763 Break this problem into two subproblems by setting (x + -1.166666667) equal to 1.6414763 and -1.6414763.Subproblem 1
x + -1.166666667 = 1.6414763 Simplifying x + -1.166666667 = 1.6414763 Reorder the terms: -1.166666667 + x = 1.6414763 Solving -1.166666667 + x = 1.6414763 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.166666667' to each side of the equation. -1.166666667 + 1.166666667 + x = 1.6414763 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + x = 1.6414763 + 1.166666667 x = 1.6414763 + 1.166666667 Combine like terms: 1.6414763 + 1.166666667 = 2.808142967 x = 2.808142967 Simplifying x = 2.808142967Subproblem 2
x + -1.166666667 = -1.6414763 Simplifying x + -1.166666667 = -1.6414763 Reorder the terms: -1.166666667 + x = -1.6414763 Solving -1.166666667 + x = -1.6414763 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.166666667' to each side of the equation. -1.166666667 + 1.166666667 + x = -1.6414763 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + x = -1.6414763 + 1.166666667 x = -1.6414763 + 1.166666667 Combine like terms: -1.6414763 + 1.166666667 = -0.474809633 x = -0.474809633 Simplifying x = -0.474809633Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.808142967, -0.474809633}Solution
x = {2.808142967, -0.474809633}
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