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Simplifying 7 + -4(x + -6) = 8 + -4x(x + -3) Reorder the terms: 7 + -4(-6 + x) = 8 + -4x(x + -3) 7 + (-6 * -4 + x * -4) = 8 + -4x(x + -3) 7 + (24 + -4x) = 8 + -4x(x + -3) Combine like terms: 7 + 24 = 31 31 + -4x = 8 + -4x(x + -3) Reorder the terms: 31 + -4x = 8 + -4x(-3 + x) 31 + -4x = 8 + (-3 * -4x + x * -4x) 31 + -4x = 8 + (12x + -4x2) Solving 31 + -4x = 8 + 12x + -4x2 Solving for variable 'x'. Reorder the terms: 31 + -8 + -4x + -12x + 4x2 = 8 + 12x + -4x2 + -8 + -12x + 4x2 Combine like terms: 31 + -8 = 23 23 + -4x + -12x + 4x2 = 8 + 12x + -4x2 + -8 + -12x + 4x2 Combine like terms: -4x + -12x = -16x 23 + -16x + 4x2 = 8 + 12x + -4x2 + -8 + -12x + 4x2 Reorder the terms: 23 + -16x + 4x2 = 8 + -8 + 12x + -12x + -4x2 + 4x2 Combine like terms: 8 + -8 = 0 23 + -16x + 4x2 = 0 + 12x + -12x + -4x2 + 4x2 23 + -16x + 4x2 = 12x + -12x + -4x2 + 4x2 Combine like terms: 12x + -12x = 0 23 + -16x + 4x2 = 0 + -4x2 + 4x2 23 + -16x + 4x2 = -4x2 + 4x2 Combine like terms: -4x2 + 4x2 = 0 23 + -16x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 5.75 + -4x + x2 = 0 Move the constant term to the right: Add '-5.75' to each side of the equation. 5.75 + -4x + -5.75 + x2 = 0 + -5.75 Reorder the terms: 5.75 + -5.75 + -4x + x2 = 0 + -5.75 Combine like terms: 5.75 + -5.75 = 0.00 0.00 + -4x + x2 = 0 + -5.75 -4x + x2 = 0 + -5.75 Combine like terms: 0 + -5.75 = -5.75 -4x + x2 = -5.75 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = -5.75 + 4 Reorder the terms: 4 + -4x + x2 = -5.75 + 4 Combine like terms: -5.75 + 4 = -1.75 4 + -4x + x2 = -1.75 Factor a perfect square on the left side: (x + -2)(x + -2) = -1.75 Can't calculate square root of the right side. The solution to this equation could not be determined.
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