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Simplifying 4[6x + -3x(x + 2)] = 2[4x + -2(x + -3)] Reorder the terms: 4[6x + -3x(2 + x)] = 2[4x + -2(x + -3)] 4[6x + (2 * -3x + x * -3x)] = 2[4x + -2(x + -3)] 4[6x + (-6x + -3x2)] = 2[4x + -2(x + -3)] Combine like terms: 6x + -6x = 0 4[0 + -3x2] = 2[4x + -2(x + -3)] 4[-3x2] = 2[4x + -2(x + -3)] Remove brackets around [-3x2] 4 * -3x2 = 2[4x + -2(x + -3)] Multiply 4 * -3 -12x2 = 2[4x + -2(x + -3)] Reorder the terms: -12x2 = 2[4x + -2(-3 + x)] -12x2 = 2[4x + (-3 * -2 + x * -2)] -12x2 = 2[4x + (6 + -2x)] Reorder the terms: -12x2 = 2[6 + 4x + -2x] Combine like terms: 4x + -2x = 2x -12x2 = 2[6 + 2x] -12x2 = [6 * 2 + 2x * 2] -12x2 = [12 + 4x] Solving -12x2 = 12 + 4x Solving for variable 'x'. Reorder the terms: -12 + -4x + -12x2 = 12 + 4x + -12 + -4x Reorder the terms: -12 + -4x + -12x2 = 12 + -12 + 4x + -4x Combine like terms: 12 + -12 = 0 -12 + -4x + -12x2 = 0 + 4x + -4x -12 + -4x + -12x2 = 4x + -4x Combine like terms: 4x + -4x = 0 -12 + -4x + -12x2 = 0 Factor out the Greatest Common Factor (GCF), '-4'. -4(3 + x + 3x2) = 0 Ignore the factor -4.Subproblem 1
Set the factor '(3 + x + 3x2)' equal to zero and attempt to solve: Simplifying 3 + x + 3x2 = 0 Solving 3 + x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1 + 0.3333333333x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 0.3333333333x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 0.3333333333x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 0.3333333333x + x2 = 0 + -1 0.3333333333x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 0.3333333333x + x2 = -1 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. 0.3333333333x + 0.25 + x2 = -1 + 0.25 Reorder the terms: 0.25 + 0.3333333333x + x2 = -1 + 0.25 Combine like terms: -1 + 0.25 = -0.75 0.25 + 0.3333333333x + x2 = -0.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -0.75 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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