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Simplifying 3x(x + -2) + -1(x + -6) = 23(x + -31) Reorder the terms: 3x(-2 + x) + -1(x + -6) = 23(x + -31) (-2 * 3x + x * 3x) + -1(x + -6) = 23(x + -31) (-6x + 3x2) + -1(x + -6) = 23(x + -31) Reorder the terms: -6x + 3x2 + -1(-6 + x) = 23(x + -31) -6x + 3x2 + (-6 * -1 + x * -1) = 23(x + -31) -6x + 3x2 + (6 + -1x) = 23(x + -31) Reorder the terms: 6 + -6x + -1x + 3x2 = 23(x + -31) Combine like terms: -6x + -1x = -7x 6 + -7x + 3x2 = 23(x + -31) Reorder the terms: 6 + -7x + 3x2 = 23(-31 + x) 6 + -7x + 3x2 = (-31 * 23 + x * 23) 6 + -7x + 3x2 = (-713 + 23x) Solving 6 + -7x + 3x2 = -713 + 23x Solving for variable 'x'. Reorder the terms: 6 + 713 + -7x + -23x + 3x2 = -713 + 23x + 713 + -23x Combine like terms: 6 + 713 = 719 719 + -7x + -23x + 3x2 = -713 + 23x + 713 + -23x Combine like terms: -7x + -23x = -30x 719 + -30x + 3x2 = -713 + 23x + 713 + -23x Reorder the terms: 719 + -30x + 3x2 = -713 + 713 + 23x + -23x Combine like terms: -713 + 713 = 0 719 + -30x + 3x2 = 0 + 23x + -23x 719 + -30x + 3x2 = 23x + -23x Combine like terms: 23x + -23x = 0 719 + -30x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 239.6666667 + -10x + x2 = 0 Move the constant term to the right: Add '-239.6666667' to each side of the equation. 239.6666667 + -10x + -239.6666667 + x2 = 0 + -239.6666667 Reorder the terms: 239.6666667 + -239.6666667 + -10x + x2 = 0 + -239.6666667 Combine like terms: 239.6666667 + -239.6666667 = 0.0000000 0.0000000 + -10x + x2 = 0 + -239.6666667 -10x + x2 = 0 + -239.6666667 Combine like terms: 0 + -239.6666667 = -239.6666667 -10x + x2 = -239.6666667 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = -239.6666667 + 25 Reorder the terms: 25 + -10x + x2 = -239.6666667 + 25 Combine like terms: -239.6666667 + 25 = -214.6666667 25 + -10x + x2 = -214.6666667 Factor a perfect square on the left side: (x + -5)(x + -5) = -214.6666667 Can't calculate square root of the right side. The solution to this equation could not be determined.
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