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Simplifying 5x(x + 1) + -2x(x + 2) = -1 + -1x Reorder the terms: 5x(1 + x) + -2x(x + 2) = -1 + -1x (1 * 5x + x * 5x) + -2x(x + 2) = -1 + -1x (5x + 5x2) + -2x(x + 2) = -1 + -1x Reorder the terms: 5x + 5x2 + -2x(2 + x) = -1 + -1x 5x + 5x2 + (2 * -2x + x * -2x) = -1 + -1x 5x + 5x2 + (-4x + -2x2) = -1 + -1x Reorder the terms: 5x + -4x + 5x2 + -2x2 = -1 + -1x Combine like terms: 5x + -4x = 1x 1x + 5x2 + -2x2 = -1 + -1x Combine like terms: 5x2 + -2x2 = 3x2 1x + 3x2 = -1 + -1x Solving 1x + 3x2 = -1 + -1x Solving for variable 'x'. Reorder the terms: 1 + 1x + x + 3x2 = -1 + -1x + 1 + x Combine like terms: 1x + x = 2x 1 + 2x + 3x2 = -1 + -1x + 1 + x Reorder the terms: 1 + 2x + 3x2 = -1 + 1 + -1x + x Combine like terms: -1 + 1 = 0 1 + 2x + 3x2 = 0 + -1x + x 1 + 2x + 3x2 = -1x + x Combine like terms: -1x + x = 0 1 + 2x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 0.3333333333 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + 0.6666666667x + -0.3333333333 + x2 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + 0.6666666667x + x2 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + 0.6666666667x + x2 = 0 + -0.3333333333 0.6666666667x + x2 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 0.6666666667x + x2 = -0.3333333333 The x term is 0.6666666667x. Take half its coefficient (0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. 0.6666666667x + 0.1111111112 + x2 = -0.3333333333 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = -0.3333333333 + 0.1111111112 Combine like terms: -0.3333333333 + 0.1111111112 = -0.2222222221 0.1111111112 + 0.6666666667x + x2 = -0.2222222221 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = -0.2222222221 Can't calculate square root of the right side. The solution to this equation could not be determined.
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