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Simplifying 21x(x + 1) + -14(x + -1) = 12x Reorder the terms: 21x(1 + x) + -14(x + -1) = 12x (1 * 21x + x * 21x) + -14(x + -1) = 12x (21x + 21x2) + -14(x + -1) = 12x Reorder the terms: 21x + 21x2 + -14(-1 + x) = 12x 21x + 21x2 + (-1 * -14 + x * -14) = 12x 21x + 21x2 + (14 + -14x) = 12x Reorder the terms: 14 + 21x + -14x + 21x2 = 12x Combine like terms: 21x + -14x = 7x 14 + 7x + 21x2 = 12x Solving 14 + 7x + 21x2 = 12x Solving for variable 'x'. Reorder the terms: 14 + 7x + -12x + 21x2 = 12x + -12x Combine like terms: 7x + -12x = -5x 14 + -5x + 21x2 = 12x + -12x Combine like terms: 12x + -12x = 0 14 + -5x + 21x2 = 0 Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. 0.6666666667 + -0.2380952381x + x2 = 0 Move the constant term to the right: Add '-0.6666666667' to each side of the equation. 0.6666666667 + -0.2380952381x + -0.6666666667 + x2 = 0 + -0.6666666667 Reorder the terms: 0.6666666667 + -0.6666666667 + -0.2380952381x + x2 = 0 + -0.6666666667 Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000 0.0000000000 + -0.2380952381x + x2 = 0 + -0.6666666667 -0.2380952381x + x2 = 0 + -0.6666666667 Combine like terms: 0 + -0.6666666667 = -0.6666666667 -0.2380952381x + x2 = -0.6666666667 The x term is -0.2380952381x. Take half its coefficient (-0.1190476191). Square it (0.01417233561) and add it to both sides. Add '0.01417233561' to each side of the equation. -0.2380952381x + 0.01417233561 + x2 = -0.6666666667 + 0.01417233561 Reorder the terms: 0.01417233561 + -0.2380952381x + x2 = -0.6666666667 + 0.01417233561 Combine like terms: -0.6666666667 + 0.01417233561 = -0.65249433109 0.01417233561 + -0.2380952381x + x2 = -0.65249433109 Factor a perfect square on the left side: (x + -0.1190476191)(x + -0.1190476191) = -0.65249433109 Can't calculate square root of the right side. The solution to this equation could not be determined.
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