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Simplifying (2x2 + 3x) + (5x2 + 5) + (6x2 + 3x + 5) = 0 Reorder the terms: (3x + 2x2) + (5x2 + 5) + (6x2 + 3x + 5) = 0 Remove parenthesis around (3x + 2x2) 3x + 2x2 + (5x2 + 5) + (6x2 + 3x + 5) = 0 Reorder the terms: 3x + 2x2 + (5 + 5x2) + (6x2 + 3x + 5) = 0 Remove parenthesis around (5 + 5x2) 3x + 2x2 + 5 + 5x2 + (6x2 + 3x + 5) = 0 Reorder the terms: 3x + 2x2 + 5 + 5x2 + (5 + 3x + 6x2) = 0 Remove parenthesis around (5 + 3x + 6x2) 3x + 2x2 + 5 + 5x2 + 5 + 3x + 6x2 = 0 Reorder the terms: 5 + 5 + 3x + 3x + 2x2 + 5x2 + 6x2 = 0 Combine like terms: 5 + 5 = 10 10 + 3x + 3x + 2x2 + 5x2 + 6x2 = 0 Combine like terms: 3x + 3x = 6x 10 + 6x + 2x2 + 5x2 + 6x2 = 0 Combine like terms: 2x2 + 5x2 = 7x2 10 + 6x + 7x2 + 6x2 = 0 Combine like terms: 7x2 + 6x2 = 13x2 10 + 6x + 13x2 = 0 Solving 10 + 6x + 13x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. 0.7692307692 + 0.4615384615x + x2 = 0 Move the constant term to the right: Add '-0.7692307692' to each side of the equation. 0.7692307692 + 0.4615384615x + -0.7692307692 + x2 = 0 + -0.7692307692 Reorder the terms: 0.7692307692 + -0.7692307692 + 0.4615384615x + x2 = 0 + -0.7692307692 Combine like terms: 0.7692307692 + -0.7692307692 = 0.0000000000 0.0000000000 + 0.4615384615x + x2 = 0 + -0.7692307692 0.4615384615x + x2 = 0 + -0.7692307692 Combine like terms: 0 + -0.7692307692 = -0.7692307692 0.4615384615x + x2 = -0.7692307692 The x term is 0.4615384615x. Take half its coefficient (0.2307692308). Square it (0.05325443788) and add it to both sides. Add '0.05325443788' to each side of the equation. 0.4615384615x + 0.05325443788 + x2 = -0.7692307692 + 0.05325443788 Reorder the terms: 0.05325443788 + 0.4615384615x + x2 = -0.7692307692 + 0.05325443788 Combine like terms: -0.7692307692 + 0.05325443788 = -0.71597633132 0.05325443788 + 0.4615384615x + x2 = -0.71597633132 Factor a perfect square on the left side: (x + 0.2307692308)(x + 0.2307692308) = -0.71597633132 Can't calculate square root of the right side. The solution to this equation could not be determined.
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