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Simplifying 0 = 12x2 + 5x + 7 Reorder the terms: 0 = 7 + 5x + 12x2 Solving 0 = 7 + 5x + 12x2 Solving for variable 'x'. Combine like terms: 0 + -7 = -7 -7 + -5x + -12x2 = 7 + 5x + 12x2 + -7 + -5x + -12x2 Reorder the terms: -7 + -5x + -12x2 = 7 + -7 + 5x + -5x + 12x2 + -12x2 Combine like terms: 7 + -7 = 0 -7 + -5x + -12x2 = 0 + 5x + -5x + 12x2 + -12x2 -7 + -5x + -12x2 = 5x + -5x + 12x2 + -12x2 Combine like terms: 5x + -5x = 0 -7 + -5x + -12x2 = 0 + 12x2 + -12x2 -7 + -5x + -12x2 = 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 -7 + -5x + -12x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(7 + 5x + 12x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(7 + 5x + 12x2)' equal to zero and attempt to solve: Simplifying 7 + 5x + 12x2 = 0 Solving 7 + 5x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 0.5833333333 + 0.4166666667x + x2 = 0 Move the constant term to the right: Add '-0.5833333333' to each side of the equation. 0.5833333333 + 0.4166666667x + -0.5833333333 + x2 = 0 + -0.5833333333 Reorder the terms: 0.5833333333 + -0.5833333333 + 0.4166666667x + x2 = 0 + -0.5833333333 Combine like terms: 0.5833333333 + -0.5833333333 = 0.0000000000 0.0000000000 + 0.4166666667x + x2 = 0 + -0.5833333333 0.4166666667x + x2 = 0 + -0.5833333333 Combine like terms: 0 + -0.5833333333 = -0.5833333333 0.4166666667x + x2 = -0.5833333333 The x term is 0.4166666667x. Take half its coefficient (0.2083333334). Square it (0.04340277781) and add it to both sides. Add '0.04340277781' to each side of the equation. 0.4166666667x + 0.04340277781 + x2 = -0.5833333333 + 0.04340277781 Reorder the terms: 0.04340277781 + 0.4166666667x + x2 = -0.5833333333 + 0.04340277781 Combine like terms: -0.5833333333 + 0.04340277781 = -0.53993055549 0.04340277781 + 0.4166666667x + x2 = -0.53993055549 Factor a perfect square on the left side: (x + 0.2083333334)(x + 0.2083333334) = -0.53993055549 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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