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Simplifying -3x(4x + 3) + 4(6x + 1) = 43 Reorder the terms: -3x(3 + 4x) + 4(6x + 1) = 43 (3 * -3x + 4x * -3x) + 4(6x + 1) = 43 (-9x + -12x2) + 4(6x + 1) = 43 Reorder the terms: -9x + -12x2 + 4(1 + 6x) = 43 -9x + -12x2 + (1 * 4 + 6x * 4) = 43 -9x + -12x2 + (4 + 24x) = 43 Reorder the terms: 4 + -9x + 24x + -12x2 = 43 Combine like terms: -9x + 24x = 15x 4 + 15x + -12x2 = 43 Solving 4 + 15x + -12x2 = 43 Solving for variable 'x'. Reorder the terms: 4 + -43 + 15x + -12x2 = 43 + -43 Combine like terms: 4 + -43 = -39 -39 + 15x + -12x2 = 43 + -43 Combine like terms: 43 + -43 = 0 -39 + 15x + -12x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-13 + 5x + -4x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-13 + 5x + -4x2)' equal to zero and attempt to solve: Simplifying -13 + 5x + -4x2 = 0 Solving -13 + 5x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 3.25 + -1.25x + x2 = 0 Move the constant term to the right: Add '-3.25' to each side of the equation. 3.25 + -1.25x + -3.25 + x2 = 0 + -3.25 Reorder the terms: 3.25 + -3.25 + -1.25x + x2 = 0 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + -1.25x + x2 = 0 + -3.25 -1.25x + x2 = 0 + -3.25 Combine like terms: 0 + -3.25 = -3.25 -1.25x + x2 = -3.25 The x term is -1.25x. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25x + 0.390625 + x2 = -3.25 + 0.390625 Reorder the terms: 0.390625 + -1.25x + x2 = -3.25 + 0.390625 Combine like terms: -3.25 + 0.390625 = -2.859375 0.390625 + -1.25x + x2 = -2.859375 Factor a perfect square on the left side: (x + -0.625)(x + -0.625) = -2.859375 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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