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Simplifying 5x(4 + -6x) = 4 + 8x (4 * 5x + -6x * 5x) = 4 + 8x (20x + -30x2) = 4 + 8x Solving 20x + -30x2 = 4 + 8x Solving for variable 'x'. Reorder the terms: -4 + 20x + -8x + -30x2 = 4 + 8x + -4 + -8x Combine like terms: 20x + -8x = 12x -4 + 12x + -30x2 = 4 + 8x + -4 + -8x Reorder the terms: -4 + 12x + -30x2 = 4 + -4 + 8x + -8x Combine like terms: 4 + -4 = 0 -4 + 12x + -30x2 = 0 + 8x + -8x -4 + 12x + -30x2 = 8x + -8x Combine like terms: 8x + -8x = 0 -4 + 12x + -30x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + 6x + -15x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + 6x + -15x2)' equal to zero and attempt to solve: Simplifying -2 + 6x + -15x2 = 0 Solving -2 + 6x + -15x2 = 0 Begin completing the square. Divide all terms by -15 the coefficient of the squared term: Divide each side by '-15'. 0.1333333333 + -0.4x + x2 = 0 Move the constant term to the right: Add '-0.1333333333' to each side of the equation. 0.1333333333 + -0.4x + -0.1333333333 + x2 = 0 + -0.1333333333 Reorder the terms: 0.1333333333 + -0.1333333333 + -0.4x + x2 = 0 + -0.1333333333 Combine like terms: 0.1333333333 + -0.1333333333 = 0.0000000000 0.0000000000 + -0.4x + x2 = 0 + -0.1333333333 -0.4x + x2 = 0 + -0.1333333333 Combine like terms: 0 + -0.1333333333 = -0.1333333333 -0.4x + x2 = -0.1333333333 The x term is -0.4x. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4x + 0.04 + x2 = -0.1333333333 + 0.04 Reorder the terms: 0.04 + -0.4x + x2 = -0.1333333333 + 0.04 Combine like terms: -0.1333333333 + 0.04 = -0.0933333333 0.04 + -0.4x + x2 = -0.0933333333 Factor a perfect square on the left side: (x + -0.2)(x + -0.2) = -0.0933333333 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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