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Simplifying 6(2x + -4) + -2(x + 1) * 15x = 0 Reorder the terms: 6(-4 + 2x) + -2(x + 1) * 15x = 0 (-4 * 6 + 2x * 6) + -2(x + 1) * 15x = 0 (-24 + 12x) + -2(x + 1) * 15x = 0 Reorder the terms: -24 + 12x + -2(1 + x) * 15x = 0 Reorder the terms for easier multiplication: -24 + 12x + -2 * 15x(1 + x) = 0 Multiply -2 * 15 -24 + 12x + -30x(1 + x) = 0 -24 + 12x + (1 * -30x + x * -30x) = 0 -24 + 12x + (-30x + -30x2) = 0 Combine like terms: 12x + -30x = -18x -24 + -18x + -30x2 = 0 Solving -24 + -18x + -30x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-6'. -6(4 + 3x + 5x2) = 0 Ignore the factor -6.Subproblem 1
Set the factor '(4 + 3x + 5x2)' equal to zero and attempt to solve: Simplifying 4 + 3x + 5x2 = 0 Solving 4 + 3x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.8 + 0.6x + x2 = 0 Move the constant term to the right: Add '-0.8' to each side of the equation. 0.8 + 0.6x + -0.8 + x2 = 0 + -0.8 Reorder the terms: 0.8 + -0.8 + 0.6x + x2 = 0 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + 0.6x + x2 = 0 + -0.8 0.6x + x2 = 0 + -0.8 Combine like terms: 0 + -0.8 = -0.8 0.6x + x2 = -0.8 The x term is 0.6x. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6x + 0.09 + x2 = -0.8 + 0.09 Reorder the terms: 0.09 + 0.6x + x2 = -0.8 + 0.09 Combine like terms: -0.8 + 0.09 = -0.71 0.09 + 0.6x + x2 = -0.71 Factor a perfect square on the left side: (x + 0.3)(x + 0.3) = -0.71 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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