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Simplifying 6x(5x + -4) = 9(2x + -5) Reorder the terms: 6x(-4 + 5x) = 9(2x + -5) (-4 * 6x + 5x * 6x) = 9(2x + -5) (-24x + 30x2) = 9(2x + -5) Reorder the terms: -24x + 30x2 = 9(-5 + 2x) -24x + 30x2 = (-5 * 9 + 2x * 9) -24x + 30x2 = (-45 + 18x) Solving -24x + 30x2 = -45 + 18x Solving for variable 'x'. Reorder the terms: 45 + -24x + -18x + 30x2 = -45 + 18x + 45 + -18x Combine like terms: -24x + -18x = -42x 45 + -42x + 30x2 = -45 + 18x + 45 + -18x Reorder the terms: 45 + -42x + 30x2 = -45 + 45 + 18x + -18x Combine like terms: -45 + 45 = 0 45 + -42x + 30x2 = 0 + 18x + -18x 45 + -42x + 30x2 = 18x + -18x Combine like terms: 18x + -18x = 0 45 + -42x + 30x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(15 + -14x + 10x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(15 + -14x + 10x2)' equal to zero and attempt to solve: Simplifying 15 + -14x + 10x2 = 0 Solving 15 + -14x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 1.5 + -1.4x + x2 = 0.0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + -1.4x + -1.5 + x2 = 0.0 + -1.5 Reorder the terms: 1.5 + -1.5 + -1.4x + x2 = 0.0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -1.4x + x2 = 0.0 + -1.5 -1.4x + x2 = 0.0 + -1.5 Combine like terms: 0.0 + -1.5 = -1.5 -1.4x + x2 = -1.5 The x term is -1.4x. Take half its coefficient (-0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. -1.4x + 0.49 + x2 = -1.5 + 0.49 Reorder the terms: 0.49 + -1.4x + x2 = -1.5 + 0.49 Combine like terms: -1.5 + 0.49 = -1.01 0.49 + -1.4x + x2 = -1.01 Factor a perfect square on the left side: (x + -0.7)(x + -0.7) = -1.01 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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