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Simplifying (3x2 + 2x + -4) + (x2 + 7) = 0 Reorder the terms: (-4 + 2x + 3x2) + (x2 + 7) = 0 Remove parenthesis around (-4 + 2x + 3x2) -4 + 2x + 3x2 + (x2 + 7) = 0 Reorder the terms: -4 + 2x + 3x2 + (7 + x2) = 0 Remove parenthesis around (7 + x2) -4 + 2x + 3x2 + 7 + x2 = 0 Reorder the terms: -4 + 7 + 2x + 3x2 + x2 = 0 Combine like terms: -4 + 7 = 3 3 + 2x + 3x2 + x2 = 0 Combine like terms: 3x2 + x2 = 4x2 3 + 2x + 4x2 = 0 Solving 3 + 2x + 4x2 = 0 Solving for variable 'x'. 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.
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