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Simplifying 4(-2x + 9) = 3x(2x + 12) Reorder the terms: 4(9 + -2x) = 3x(2x + 12) (9 * 4 + -2x * 4) = 3x(2x + 12) (36 + -8x) = 3x(2x + 12) Reorder the terms: 36 + -8x = 3x(12 + 2x) 36 + -8x = (12 * 3x + 2x * 3x) 36 + -8x = (36x + 6x2) Solving 36 + -8x = 36x + 6x2 Solving for variable 'x'. Combine like terms: -8x + -36x = -44x 36 + -44x + -6x2 = 36x + 6x2 + -36x + -6x2 Reorder the terms: 36 + -44x + -6x2 = 36x + -36x + 6x2 + -6x2 Combine like terms: 36x + -36x = 0 36 + -44x + -6x2 = 0 + 6x2 + -6x2 36 + -44x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 36 + -44x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(18 + -22x + -3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(18 + -22x + -3x2)' equal to zero and attempt to solve: Simplifying 18 + -22x + -3x2 = 0 Solving 18 + -22x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -6 + 7.333333333x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + 7.333333333x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + 7.333333333x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 7.333333333x + x2 = 0 + 6 7.333333333x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 7.333333333x + x2 = 6 The x term is 7.333333333x. Take half its coefficient (3.666666667). Square it (13.44444445) and add it to both sides. Add '13.44444445' to each side of the equation. 7.333333333x + 13.44444445 + x2 = 6 + 13.44444445 Reorder the terms: 13.44444445 + 7.333333333x + x2 = 6 + 13.44444445 Combine like terms: 6 + 13.44444445 = 19.44444445 13.44444445 + 7.333333333x + x2 = 19.44444445 Factor a perfect square on the left side: (x + 3.666666667)(x + 3.666666667) = 19.44444445 Calculate the square root of the right side: 4.409585519 Break this problem into two subproblems by setting (x + 3.666666667) equal to 4.409585519 and -4.409585519.Subproblem 1
x + 3.666666667 = 4.409585519 Simplifying x + 3.666666667 = 4.409585519 Reorder the terms: 3.666666667 + x = 4.409585519 Solving 3.666666667 + x = 4.409585519 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.666666667' to each side of the equation. 3.666666667 + -3.666666667 + x = 4.409585519 + -3.666666667 Combine like terms: 3.666666667 + -3.666666667 = 0.000000000 0.000000000 + x = 4.409585519 + -3.666666667 x = 4.409585519 + -3.666666667 Combine like terms: 4.409585519 + -3.666666667 = 0.742918852 x = 0.742918852 Simplifying x = 0.742918852Subproblem 2
x + 3.666666667 = -4.409585519 Simplifying x + 3.666666667 = -4.409585519 Reorder the terms: 3.666666667 + x = -4.409585519 Solving 3.666666667 + x = -4.409585519 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.666666667' to each side of the equation. 3.666666667 + -3.666666667 + x = -4.409585519 + -3.666666667 Combine like terms: 3.666666667 + -3.666666667 = 0.000000000 0.000000000 + x = -4.409585519 + -3.666666667 x = -4.409585519 + -3.666666667 Combine like terms: -4.409585519 + -3.666666667 = -8.076252186 x = -8.076252186 Simplifying x = -8.076252186Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.742918852, -8.076252186}Solution
x = {0.742918852, -8.076252186}
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