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Simplifying 3x(4x + -10) = -126 Reorder the terms: 3x(-10 + 4x) = -126 (-10 * 3x + 4x * 3x) = -126 (-30x + 12x2) = -126 Solving -30x + 12x2 = -126 Solving for variable 'x'. Reorder the terms: 126 + -30x + 12x2 = -126 + 126 Combine like terms: -126 + 126 = 0 126 + -30x + 12x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(21 + -5x + 2x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(21 + -5x + 2x2)' equal to zero and attempt to solve: Simplifying 21 + -5x + 2x2 = 0 Solving 21 + -5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 10.5 + -2.5x + x2 = 0 Move the constant term to the right: Add '-10.5' to each side of the equation. 10.5 + -2.5x + -10.5 + x2 = 0 + -10.5 Reorder the terms: 10.5 + -10.5 + -2.5x + x2 = 0 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + -2.5x + x2 = 0 + -10.5 -2.5x + x2 = 0 + -10.5 Combine like terms: 0 + -10.5 = -10.5 -2.5x + x2 = -10.5 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = -10.5 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = -10.5 + 1.5625 Combine like terms: -10.5 + 1.5625 = -8.9375 1.5625 + -2.5x + x2 = -8.9375 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = -8.9375 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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