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Simplifying 3(x2 + 1) = 5x + -6x2 Reorder the terms: 3(1 + x2) = 5x + -6x2 (1 * 3 + x2 * 3) = 5x + -6x2 (3 + 3x2) = 5x + -6x2 Solving 3 + 3x2 = 5x + -6x2 Solving for variable 'x'. Reorder the terms: 3 + -5x + 3x2 + 6x2 = 5x + -6x2 + -5x + 6x2 Combine like terms: 3x2 + 6x2 = 9x2 3 + -5x + 9x2 = 5x + -6x2 + -5x + 6x2 Reorder the terms: 3 + -5x + 9x2 = 5x + -5x + -6x2 + 6x2 Combine like terms: 5x + -5x = 0 3 + -5x + 9x2 = 0 + -6x2 + 6x2 3 + -5x + 9x2 = -6x2 + 6x2 Combine like terms: -6x2 + 6x2 = 0 3 + -5x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.3333333333 + -0.5555555556x + x2 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + -0.5555555556x + -0.3333333333 + x2 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + -0.5555555556x + x2 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + -0.5555555556x + x2 = 0 + -0.3333333333 -0.5555555556x + x2 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 -0.5555555556x + x2 = -0.3333333333 The x term is -0.5555555556x. Take half its coefficient (-0.2777777778). Square it (0.07716049384) and add it to both sides. Add '0.07716049384' to each side of the equation. -0.5555555556x + 0.07716049384 + x2 = -0.3333333333 + 0.07716049384 Reorder the terms: 0.07716049384 + -0.5555555556x + x2 = -0.3333333333 + 0.07716049384 Combine like terms: -0.3333333333 + 0.07716049384 = -0.25617283946 0.07716049384 + -0.5555555556x + x2 = -0.25617283946 Factor a perfect square on the left side: (x + -0.2777777778)(x + -0.2777777778) = -0.25617283946 Can't calculate square root of the right side. The solution to this equation could not be determined.
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