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Simplifying 3(2x + -3) = 4x(x + 4) Reorder the terms: 3(-3 + 2x) = 4x(x + 4) (-3 * 3 + 2x * 3) = 4x(x + 4) (-9 + 6x) = 4x(x + 4) Reorder the terms: -9 + 6x = 4x(4 + x) -9 + 6x = (4 * 4x + x * 4x) -9 + 6x = (16x + 4x2) Solving -9 + 6x = 16x + 4x2 Solving for variable 'x'. Combine like terms: 6x + -16x = -10x -9 + -10x + -4x2 = 16x + 4x2 + -16x + -4x2 Reorder the terms: -9 + -10x + -4x2 = 16x + -16x + 4x2 + -4x2 Combine like terms: 16x + -16x = 0 -9 + -10x + -4x2 = 0 + 4x2 + -4x2 -9 + -10x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -9 + -10x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(9 + 10x + 4x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(9 + 10x + 4x2)' equal to zero and attempt to solve: Simplifying 9 + 10x + 4x2 = 0 Solving 9 + 10x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 2.25 + 2.5x + x2 = 0 Move the constant term to the right: Add '-2.25' to each side of the equation. 2.25 + 2.5x + -2.25 + x2 = 0 + -2.25 Reorder the terms: 2.25 + -2.25 + 2.5x + x2 = 0 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + 2.5x + x2 = 0 + -2.25 2.5x + x2 = 0 + -2.25 Combine like terms: 0 + -2.25 = -2.25 2.5x + x2 = -2.25 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = -2.25 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = -2.25 + 1.5625 Combine like terms: -2.25 + 1.5625 = -0.6875 1.5625 + 2.5x + x2 = -0.6875 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = -0.6875 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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