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Simplifying 0 = 2x + 3x + 3 + 4x2 + 10 + x Reorder the terms: 0 = 3 + 10 + 2x + 3x + x + 4x2 Combine like terms: 3 + 10 = 13 0 = 13 + 2x + 3x + x + 4x2 Combine like terms: 2x + 3x = 5x 0 = 13 + 5x + x + 4x2 Combine like terms: 5x + x = 6x 0 = 13 + 6x + 4x2 Solving 0 = 13 + 6x + 4x2 Solving for variable 'x'. Combine like terms: 0 + -13 = -13 -13 + -6x + -4x2 = 13 + 6x + 4x2 + -13 + -6x + -4x2 Reorder the terms: -13 + -6x + -4x2 = 13 + -13 + 6x + -6x + 4x2 + -4x2 Combine like terms: 13 + -13 = 0 -13 + -6x + -4x2 = 0 + 6x + -6x + 4x2 + -4x2 -13 + -6x + -4x2 = 6x + -6x + 4x2 + -4x2 Combine like terms: 6x + -6x = 0 -13 + -6x + -4x2 = 0 + 4x2 + -4x2 -13 + -6x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -13 + -6x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(13 + 6x + 4x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(13 + 6x + 4x2)' equal to zero and attempt to solve: Simplifying 13 + 6x + 4x2 = 0 Solving 13 + 6x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 3.25 + 1.5x + x2 = 0 Move the constant term to the right: Add '-3.25' to each side of the equation. 3.25 + 1.5x + -3.25 + x2 = 0 + -3.25 Reorder the terms: 3.25 + -3.25 + 1.5x + x2 = 0 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + 1.5x + x2 = 0 + -3.25 1.5x + x2 = 0 + -3.25 Combine like terms: 0 + -3.25 = -3.25 1.5x + x2 = -3.25 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = -3.25 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = -3.25 + 0.5625 Combine like terms: -3.25 + 0.5625 = -2.6875 0.5625 + 1.5x + x2 = -2.6875 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = -2.6875 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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