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Simplifying (5x2 + 6x + 8) + (6x2 + 9x) = 0 Reorder the terms: (8 + 6x + 5x2) + (6x2 + 9x) = 0 Remove parenthesis around (8 + 6x + 5x2) 8 + 6x + 5x2 + (6x2 + 9x) = 0 Reorder the terms: 8 + 6x + 5x2 + (9x + 6x2) = 0 Remove parenthesis around (9x + 6x2) 8 + 6x + 5x2 + 9x + 6x2 = 0 Reorder the terms: 8 + 6x + 9x + 5x2 + 6x2 = 0 Combine like terms: 6x + 9x = 15x 8 + 15x + 5x2 + 6x2 = 0 Combine like terms: 5x2 + 6x2 = 11x2 8 + 15x + 11x2 = 0 Solving 8 + 15x + 11x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. 0.7272727273 + 1.363636364x + x2 = 0 Move the constant term to the right: Add '-0.7272727273' to each side of the equation. 0.7272727273 + 1.363636364x + -0.7272727273 + x2 = 0 + -0.7272727273 Reorder the terms: 0.7272727273 + -0.7272727273 + 1.363636364x + x2 = 0 + -0.7272727273 Combine like terms: 0.7272727273 + -0.7272727273 = 0.0000000000 0.0000000000 + 1.363636364x + x2 = 0 + -0.7272727273 1.363636364x + x2 = 0 + -0.7272727273 Combine like terms: 0 + -0.7272727273 = -0.7272727273 1.363636364x + x2 = -0.7272727273 The x term is 1.363636364x. Take half its coefficient (0.681818182). Square it (0.4648760333) and add it to both sides. Add '0.4648760333' to each side of the equation. 1.363636364x + 0.4648760333 + x2 = -0.7272727273 + 0.4648760333 Reorder the terms: 0.4648760333 + 1.363636364x + x2 = -0.7272727273 + 0.4648760333 Combine like terms: -0.7272727273 + 0.4648760333 = -0.262396694 0.4648760333 + 1.363636364x + x2 = -0.262396694 Factor a perfect square on the left side: (x + 0.681818182)(x + 0.681818182) = -0.262396694 Can't calculate square root of the right side. The solution to this equation could not be determined.
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