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Simplifying (4x2 + -2x + 5) + -1(x2 + 6x + -2) = 0 Reorder the terms: (5 + -2x + 4x2) + -1(x2 + 6x + -2) = 0 Remove parenthesis around (5 + -2x + 4x2) 5 + -2x + 4x2 + -1(x2 + 6x + -2) = 0 Reorder the terms: 5 + -2x + 4x2 + -1(-2 + 6x + x2) = 0 5 + -2x + 4x2 + (-2 * -1 + 6x * -1 + x2 * -1) = 0 5 + -2x + 4x2 + (2 + -6x + -1x2) = 0 Reorder the terms: 5 + 2 + -2x + -6x + 4x2 + -1x2 = 0 Combine like terms: 5 + 2 = 7 7 + -2x + -6x + 4x2 + -1x2 = 0 Combine like terms: -2x + -6x = -8x 7 + -8x + 4x2 + -1x2 = 0 Combine like terms: 4x2 + -1x2 = 3x2 7 + -8x + 3x2 = 0 Solving 7 + -8x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 2.333333333 + -2.666666667x + x2 = 0 Move the constant term to the right: Add '-2.333333333' to each side of the equation. 2.333333333 + -2.666666667x + -2.333333333 + x2 = 0 + -2.333333333 Reorder the terms: 2.333333333 + -2.333333333 + -2.666666667x + x2 = 0 + -2.333333333 Combine like terms: 2.333333333 + -2.333333333 = 0.000000000 0.000000000 + -2.666666667x + x2 = 0 + -2.333333333 -2.666666667x + x2 = 0 + -2.333333333 Combine like terms: 0 + -2.333333333 = -2.333333333 -2.666666667x + x2 = -2.333333333 The x term is -2.666666667x. Take half its coefficient (-1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. -2.666666667x + 1.777777780 + x2 = -2.333333333 + 1.777777780 Reorder the terms: 1.777777780 + -2.666666667x + x2 = -2.333333333 + 1.777777780 Combine like terms: -2.333333333 + 1.777777780 = -0.555555553 1.777777780 + -2.666666667x + x2 = -0.555555553 Factor a perfect square on the left side: (x + -1.333333334)(x + -1.333333334) = -0.555555553 Can't calculate square root of the right side. The solution to this equation could not be determined.
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