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Simplifying -5x(2x + -6) = 4(x + 11) Reorder the terms: -5x(-6 + 2x) = 4(x + 11) (-6 * -5x + 2x * -5x) = 4(x + 11) (30x + -10x2) = 4(x + 11) Reorder the terms: 30x + -10x2 = 4(11 + x) 30x + -10x2 = (11 * 4 + x * 4) 30x + -10x2 = (44 + 4x) Solving 30x + -10x2 = 44 + 4x Solving for variable 'x'. Reorder the terms: -44 + 30x + -4x + -10x2 = 44 + 4x + -44 + -4x Combine like terms: 30x + -4x = 26x -44 + 26x + -10x2 = 44 + 4x + -44 + -4x Reorder the terms: -44 + 26x + -10x2 = 44 + -44 + 4x + -4x Combine like terms: 44 + -44 = 0 -44 + 26x + -10x2 = 0 + 4x + -4x -44 + 26x + -10x2 = 4x + -4x Combine like terms: 4x + -4x = 0 -44 + 26x + -10x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-22 + 13x + -5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-22 + 13x + -5x2)' equal to zero and attempt to solve: Simplifying -22 + 13x + -5x2 = 0 Solving -22 + 13x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 4.4 + -2.6x + x2 = 0 Move the constant term to the right: Add '-4.4' to each side of the equation. 4.4 + -2.6x + -4.4 + x2 = 0 + -4.4 Reorder the terms: 4.4 + -4.4 + -2.6x + x2 = 0 + -4.4 Combine like terms: 4.4 + -4.4 = 0.0 0.0 + -2.6x + x2 = 0 + -4.4 -2.6x + x2 = 0 + -4.4 Combine like terms: 0 + -4.4 = -4.4 -2.6x + x2 = -4.4 The x term is -2.6x. Take half its coefficient (-1.3). Square it (1.69) and add it to both sides. Add '1.69' to each side of the equation. -2.6x + 1.69 + x2 = -4.4 + 1.69 Reorder the terms: 1.69 + -2.6x + x2 = -4.4 + 1.69 Combine like terms: -4.4 + 1.69 = -2.71 1.69 + -2.6x + x2 = -2.71 Factor a perfect square on the left side: (x + -1.3)(x + -1.3) = -2.71 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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