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Simplifying 4x(x + -3) = 3(2x + -10) Reorder the terms: 4x(-3 + x) = 3(2x + -10) (-3 * 4x + x * 4x) = 3(2x + -10) (-12x + 4x2) = 3(2x + -10) Reorder the terms: -12x + 4x2 = 3(-10 + 2x) -12x + 4x2 = (-10 * 3 + 2x * 3) -12x + 4x2 = (-30 + 6x) Solving -12x + 4x2 = -30 + 6x Solving for variable 'x'. Reorder the terms: 30 + -12x + -6x + 4x2 = -30 + 6x + 30 + -6x Combine like terms: -12x + -6x = -18x 30 + -18x + 4x2 = -30 + 6x + 30 + -6x Reorder the terms: 30 + -18x + 4x2 = -30 + 30 + 6x + -6x Combine like terms: -30 + 30 = 0 30 + -18x + 4x2 = 0 + 6x + -6x 30 + -18x + 4x2 = 6x + -6x Combine like terms: 6x + -6x = 0 30 + -18x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(15 + -9x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(15 + -9x + 2x2)' equal to zero and attempt to solve: Simplifying 15 + -9x + 2x2 = 0 Solving 15 + -9x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 7.5 + -4.5x + x2 = 0 Move the constant term to the right: Add '-7.5' to each side of the equation. 7.5 + -4.5x + -7.5 + x2 = 0 + -7.5 Reorder the terms: 7.5 + -7.5 + -4.5x + x2 = 0 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + -4.5x + x2 = 0 + -7.5 -4.5x + x2 = 0 + -7.5 Combine like terms: 0 + -7.5 = -7.5 -4.5x + x2 = -7.5 The x term is -4.5x. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5x + 5.0625 + x2 = -7.5 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = -7.5 + 5.0625 Combine like terms: -7.5 + 5.0625 = -2.4375 5.0625 + -4.5x + x2 = -2.4375 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = -2.4375 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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