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Simplifying 0 = 4x2 + 2x + 3 Reorder the terms: 0 = 3 + 2x + 4x2 Solving 0 = 3 + 2x + 4x2 Solving for variable 'x'. Combine like terms: 0 + -3 = -3 -3 + -2x + -4x2 = 3 + 2x + 4x2 + -3 + -2x + -4x2 Reorder the terms: -3 + -2x + -4x2 = 3 + -3 + 2x + -2x + 4x2 + -4x2 Combine like terms: 3 + -3 = 0 -3 + -2x + -4x2 = 0 + 2x + -2x + 4x2 + -4x2 -3 + -2x + -4x2 = 2x + -2x + 4x2 + -4x2 Combine like terms: 2x + -2x = 0 -3 + -2x + -4x2 = 0 + 4x2 + -4x2 -3 + -2x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -3 + -2x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(3 + 2x + 4x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(3 + 2x + 4x2)' equal to zero and attempt to solve: Simplifying 3 + 2x + 4x2 = 0 Solving 3 + 2x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.75 + 0.5x + x2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + 0.5x + -0.75 + x2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + 0.5x + x2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + 0.5x + x2 = 0 + -0.75 0.5x + x2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 0.5x + x2 = -0.75 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = -0.75 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = -0.75 + 0.0625 Combine like terms: -0.75 + 0.0625 = -0.6875 0.0625 + 0.5x + x2 = -0.6875 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = -0.6875 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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