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Simplifying 0 = 4x2 + 12x + 13 Reorder the terms: 0 = 13 + 12x + 4x2 Solving 0 = 13 + 12x + 4x2 Solving for variable 'x'. Combine like terms: 0 + -13 = -13 -13 + -12x + -4x2 = 13 + 12x + 4x2 + -13 + -12x + -4x2 Reorder the terms: -13 + -12x + -4x2 = 13 + -13 + 12x + -12x + 4x2 + -4x2 Combine like terms: 13 + -13 = 0 -13 + -12x + -4x2 = 0 + 12x + -12x + 4x2 + -4x2 -13 + -12x + -4x2 = 12x + -12x + 4x2 + -4x2 Combine like terms: 12x + -12x = 0 -13 + -12x + -4x2 = 0 + 4x2 + -4x2 -13 + -12x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -13 + -12x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(13 + 12x + 4x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(13 + 12x + 4x2)' equal to zero and attempt to solve: Simplifying 13 + 12x + 4x2 = 0 Solving 13 + 12x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 3.25 + 3x + x2 = 0 Move the constant term to the right: Add '-3.25' to each side of the equation. 3.25 + 3x + -3.25 + x2 = 0 + -3.25 Reorder the terms: 3.25 + -3.25 + 3x + x2 = 0 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + 3x + x2 = 0 + -3.25 3x + x2 = 0 + -3.25 Combine like terms: 0 + -3.25 = -3.25 3x + x2 = -3.25 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = -3.25 + 2.25 Reorder the terms: 2.25 + 3x + x2 = -3.25 + 2.25 Combine like terms: -3.25 + 2.25 = -1 2.25 + 3x + x2 = -1 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = -1 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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