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Simplifying 4x(x + -2) + -3(2x + -6) = 0 Reorder the terms: 4x(-2 + x) + -3(2x + -6) = 0 (-2 * 4x + x * 4x) + -3(2x + -6) = 0 (-8x + 4x2) + -3(2x + -6) = 0 Reorder the terms: -8x + 4x2 + -3(-6 + 2x) = 0 -8x + 4x2 + (-6 * -3 + 2x * -3) = 0 -8x + 4x2 + (18 + -6x) = 0 Reorder the terms: 18 + -8x + -6x + 4x2 = 0 Combine like terms: -8x + -6x = -14x 18 + -14x + 4x2 = 0 Solving 18 + -14x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(9 + -7x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(9 + -7x + 2x2)' equal to zero and attempt to solve: Simplifying 9 + -7x + 2x2 = 0 Solving 9 + -7x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 4.5 + -3.5x + x2 = 0 Move the constant term to the right: Add '-4.5' to each side of the equation. 4.5 + -3.5x + -4.5 + x2 = 0 + -4.5 Reorder the terms: 4.5 + -4.5 + -3.5x + x2 = 0 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + -3.5x + x2 = 0 + -4.5 -3.5x + x2 = 0 + -4.5 Combine like terms: 0 + -4.5 = -4.5 -3.5x + x2 = -4.5 The x term is -3.5x. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5x + 3.0625 + x2 = -4.5 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = -4.5 + 3.0625 Combine like terms: -4.5 + 3.0625 = -1.4375 3.0625 + -3.5x + x2 = -1.4375 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = -1.4375 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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