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Simplifying 3x(x + -6) = 6x + -90 Reorder the terms: 3x(-6 + x) = 6x + -90 (-6 * 3x + x * 3x) = 6x + -90 (-18x + 3x2) = 6x + -90 Reorder the terms: -18x + 3x2 = -90 + 6x Solving -18x + 3x2 = -90 + 6x Solving for variable 'x'. Reorder the terms: 90 + -18x + -6x + 3x2 = -90 + 6x + 90 + -6x Combine like terms: -18x + -6x = -24x 90 + -24x + 3x2 = -90 + 6x + 90 + -6x Reorder the terms: 90 + -24x + 3x2 = -90 + 90 + 6x + -6x Combine like terms: -90 + 90 = 0 90 + -24x + 3x2 = 0 + 6x + -6x 90 + -24x + 3x2 = 6x + -6x Combine like terms: 6x + -6x = 0 90 + -24x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(30 + -8x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(30 + -8x + x2)' equal to zero and attempt to solve: Simplifying 30 + -8x + x2 = 0 Solving 30 + -8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-30' to each side of the equation. 30 + -8x + -30 + x2 = 0 + -30 Reorder the terms: 30 + -30 + -8x + x2 = 0 + -30 Combine like terms: 30 + -30 = 0 0 + -8x + x2 = 0 + -30 -8x + x2 = 0 + -30 Combine like terms: 0 + -30 = -30 -8x + x2 = -30 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = -30 + 16 Reorder the terms: 16 + -8x + x2 = -30 + 16 Combine like terms: -30 + 16 = -14 16 + -8x + x2 = -14 Factor a perfect square on the left side: (x + -4)(x + -4) = -14 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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