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Simplifying (6x + -3)(2x + 4) = 12(x + 1) Reorder the terms: (-3 + 6x)(2x + 4) = 12(x + 1) Reorder the terms: (-3 + 6x)(4 + 2x) = 12(x + 1) Multiply (-3 + 6x) * (4 + 2x) (-3(4 + 2x) + 6x * (4 + 2x)) = 12(x + 1) ((4 * -3 + 2x * -3) + 6x * (4 + 2x)) = 12(x + 1) ((-12 + -6x) + 6x * (4 + 2x)) = 12(x + 1) (-12 + -6x + (4 * 6x + 2x * 6x)) = 12(x + 1) (-12 + -6x + (24x + 12x2)) = 12(x + 1) Combine like terms: -6x + 24x = 18x (-12 + 18x + 12x2) = 12(x + 1) Reorder the terms: -12 + 18x + 12x2 = 12(1 + x) -12 + 18x + 12x2 = (1 * 12 + x * 12) -12 + 18x + 12x2 = (12 + 12x) Solving -12 + 18x + 12x2 = 12 + 12x Solving for variable 'x'. Reorder the terms: -12 + -12 + 18x + -12x + 12x2 = 12 + 12x + -12 + -12x Combine like terms: -12 + -12 = -24 -24 + 18x + -12x + 12x2 = 12 + 12x + -12 + -12x Combine like terms: 18x + -12x = 6x -24 + 6x + 12x2 = 12 + 12x + -12 + -12x Reorder the terms: -24 + 6x + 12x2 = 12 + -12 + 12x + -12x Combine like terms: 12 + -12 = 0 -24 + 6x + 12x2 = 0 + 12x + -12x -24 + 6x + 12x2 = 12x + -12x Combine like terms: 12x + -12x = 0 -24 + 6x + 12x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-4 + x + 2x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-4 + x + 2x2)' equal to zero and attempt to solve: Simplifying -4 + x + 2x2 = 0 Solving -4 + x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2 + 0.5x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 0.5x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 0.5x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 0.5x + x2 = 0 + 2 0.5x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 0.5x + x2 = 2 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.5x + 0.25 + x2 = 2 + 0.25 Reorder the terms: 0.25 + 0.5x + x2 = 2 + 0.25 Combine like terms: 2 + 0.25 = 2.25 0.25 + 0.5x + x2 = 2.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 2.25 Calculate the square root of the right side: 1.5 Break this problem into two subproblems by setting (x + 0.5) equal to 1.5 and -1.5.Subproblem 1
x + 0.5 = 1.5 Simplifying x + 0.5 = 1.5 Reorder the terms: 0.5 + x = 1.5 Solving 0.5 + x = 1.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 1.5 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.5 + -0.5 x = 1.5 + -0.5 Combine like terms: 1.5 + -0.5 = 1 x = 1 Simplifying x = 1Subproblem 2
x + 0.5 = -1.5 Simplifying x + 0.5 = -1.5 Reorder the terms: 0.5 + x = -1.5 Solving 0.5 + x = -1.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -1.5 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.5 + -0.5 x = -1.5 + -0.5 Combine like terms: -1.5 + -0.5 = -2 x = -2 Simplifying x = -2Solution
The solution to the problem is based on the solutions from the subproblems. x = {1, -2}Solution
x = {1, -2}
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