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Simplifying x(6x + -1) = 6x + 1(x + -5) Reorder the terms: x(-1 + 6x) = 6x + 1(x + -5) (-1 * x + 6x * x) = 6x + 1(x + -5) (-1x + 6x2) = 6x + 1(x + -5) Reorder the terms: -1x + 6x2 = 6x + 1(-5 + x) -1x + 6x2 = 6x + (-5 * 1 + x * 1) -1x + 6x2 = 6x + (-5 + 1x) Reorder the terms: -1x + 6x2 = -5 + 6x + 1x Combine like terms: 6x + 1x = 7x -1x + 6x2 = -5 + 7x Solving -1x + 6x2 = -5 + 7x Solving for variable 'x'. Reorder the terms: 5 + -1x + -7x + 6x2 = -5 + 7x + 5 + -7x Combine like terms: -1x + -7x = -8x 5 + -8x + 6x2 = -5 + 7x + 5 + -7x Reorder the terms: 5 + -8x + 6x2 = -5 + 5 + 7x + -7x Combine like terms: -5 + 5 = 0 5 + -8x + 6x2 = 0 + 7x + -7x 5 + -8x + 6x2 = 7x + -7x Combine like terms: 7x + -7x = 0 5 + -8x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.8333333333 + -1.333333333x + x2 = 0 Move the constant term to the right: Add '-0.8333333333' to each side of the equation. 0.8333333333 + -1.333333333x + -0.8333333333 + x2 = 0 + -0.8333333333 Reorder the terms: 0.8333333333 + -0.8333333333 + -1.333333333x + x2 = 0 + -0.8333333333 Combine like terms: 0.8333333333 + -0.8333333333 = 0.0000000000 0.0000000000 + -1.333333333x + x2 = 0 + -0.8333333333 -1.333333333x + x2 = 0 + -0.8333333333 Combine like terms: 0 + -0.8333333333 = -0.8333333333 -1.333333333x + x2 = -0.8333333333 The x term is -1.333333333x. Take half its coefficient (-0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. -1.333333333x + 0.4444444442 + x2 = -0.8333333333 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333x + x2 = -0.8333333333 + 0.4444444442 Combine like terms: -0.8333333333 + 0.4444444442 = -0.3888888891 0.4444444442 + -1.333333333x + x2 = -0.3888888891 Factor a perfect square on the left side: (x + -0.6666666665)(x + -0.6666666665) = -0.3888888891 Can't calculate square root of the right side. The solution to this equation could not be determined.
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