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Simplifying 0 = 12x2 + 9x + 4 Reorder the terms: 0 = 4 + 9x + 12x2 Solving 0 = 4 + 9x + 12x2 Solving for variable 'x'. Combine like terms: 0 + -4 = -4 -4 + -9x + -12x2 = 4 + 9x + 12x2 + -4 + -9x + -12x2 Reorder the terms: -4 + -9x + -12x2 = 4 + -4 + 9x + -9x + 12x2 + -12x2 Combine like terms: 4 + -4 = 0 -4 + -9x + -12x2 = 0 + 9x + -9x + 12x2 + -12x2 -4 + -9x + -12x2 = 9x + -9x + 12x2 + -12x2 Combine like terms: 9x + -9x = 0 -4 + -9x + -12x2 = 0 + 12x2 + -12x2 -4 + -9x + -12x2 = 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 -4 + -9x + -12x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(4 + 9x + 12x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(4 + 9x + 12x2)' equal to zero and attempt to solve: Simplifying 4 + 9x + 12x2 = 0 Solving 4 + 9x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 0.3333333333 + 0.75x + x2 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + 0.75x + -0.3333333333 + x2 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + 0.75x + x2 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + 0.75x + x2 = 0 + -0.3333333333 0.75x + x2 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 0.75x + x2 = -0.3333333333 The x term is 0.75x. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75x + 0.140625 + x2 = -0.3333333333 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = -0.3333333333 + 0.140625 Combine like terms: -0.3333333333 + 0.140625 = -0.1927083333 0.140625 + 0.75x + x2 = -0.1927083333 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = -0.1927083333 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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