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Simplifying 3(3x + -1) + 3(3x + -1) = 5x(2x + 2) Reorder the terms: 3(-1 + 3x) + 3(3x + -1) = 5x(2x + 2) (-1 * 3 + 3x * 3) + 3(3x + -1) = 5x(2x + 2) (-3 + 9x) + 3(3x + -1) = 5x(2x + 2) Reorder the terms: -3 + 9x + 3(-1 + 3x) = 5x(2x + 2) -3 + 9x + (-1 * 3 + 3x * 3) = 5x(2x + 2) -3 + 9x + (-3 + 9x) = 5x(2x + 2) Reorder the terms: -3 + -3 + 9x + 9x = 5x(2x + 2) Combine like terms: -3 + -3 = -6 -6 + 9x + 9x = 5x(2x + 2) Combine like terms: 9x + 9x = 18x -6 + 18x = 5x(2x + 2) Reorder the terms: -6 + 18x = 5x(2 + 2x) -6 + 18x = (2 * 5x + 2x * 5x) -6 + 18x = (10x + 10x2) Solving -6 + 18x = 10x + 10x2 Solving for variable 'x'. Combine like terms: 18x + -10x = 8x -6 + 8x + -10x2 = 10x + 10x2 + -10x + -10x2 Reorder the terms: -6 + 8x + -10x2 = 10x + -10x + 10x2 + -10x2 Combine like terms: 10x + -10x = 0 -6 + 8x + -10x2 = 0 + 10x2 + -10x2 -6 + 8x + -10x2 = 10x2 + -10x2 Combine like terms: 10x2 + -10x2 = 0 -6 + 8x + -10x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + 4x + -5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + 4x + -5x2)' equal to zero and attempt to solve: Simplifying -3 + 4x + -5x2 = 0 Solving -3 + 4x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 0.6 + -0.8x + x2 = 0 Move the constant term to the right: Add '-0.6' to each side of the equation. 0.6 + -0.8x + -0.6 + x2 = 0 + -0.6 Reorder the terms: 0.6 + -0.6 + -0.8x + x2 = 0 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + -0.8x + x2 = 0 + -0.6 -0.8x + x2 = 0 + -0.6 Combine like terms: 0 + -0.6 = -0.6 -0.8x + x2 = -0.6 The x term is -0.8x. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8x + 0.16 + x2 = -0.6 + 0.16 Reorder the terms: 0.16 + -0.8x + x2 = -0.6 + 0.16 Combine like terms: -0.6 + 0.16 = -0.44 0.16 + -0.8x + x2 = -0.44 Factor a perfect square on the left side: (x + -0.4)(x + -0.4) = -0.44 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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