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Simplifying (4x + 7)(x + -1) = 2(x + -21) Reorder the terms: (7 + 4x)(x + -1) = 2(x + -21) Reorder the terms: (7 + 4x)(-1 + x) = 2(x + -21) Multiply (7 + 4x) * (-1 + x) (7(-1 + x) + 4x * (-1 + x)) = 2(x + -21) ((-1 * 7 + x * 7) + 4x * (-1 + x)) = 2(x + -21) ((-7 + 7x) + 4x * (-1 + x)) = 2(x + -21) (-7 + 7x + (-1 * 4x + x * 4x)) = 2(x + -21) (-7 + 7x + (-4x + 4x2)) = 2(x + -21) Combine like terms: 7x + -4x = 3x (-7 + 3x + 4x2) = 2(x + -21) Reorder the terms: -7 + 3x + 4x2 = 2(-21 + x) -7 + 3x + 4x2 = (-21 * 2 + x * 2) -7 + 3x + 4x2 = (-42 + 2x) Solving -7 + 3x + 4x2 = -42 + 2x Solving for variable 'x'. Reorder the terms: -7 + 42 + 3x + -2x + 4x2 = -42 + 2x + 42 + -2x Combine like terms: -7 + 42 = 35 35 + 3x + -2x + 4x2 = -42 + 2x + 42 + -2x Combine like terms: 3x + -2x = 1x 35 + 1x + 4x2 = -42 + 2x + 42 + -2x Reorder the terms: 35 + 1x + 4x2 = -42 + 42 + 2x + -2x Combine like terms: -42 + 42 = 0 35 + 1x + 4x2 = 0 + 2x + -2x 35 + 1x + 4x2 = 2x + -2x Combine like terms: 2x + -2x = 0 35 + 1x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 8.75 + 0.25x + x2 = 0 Move the constant term to the right: Add '-8.75' to each side of the equation. 8.75 + 0.25x + -8.75 + x2 = 0 + -8.75 Reorder the terms: 8.75 + -8.75 + 0.25x + x2 = 0 + -8.75 Combine like terms: 8.75 + -8.75 = 0.00 0.00 + 0.25x + x2 = 0 + -8.75 0.25x + x2 = 0 + -8.75 Combine like terms: 0 + -8.75 = -8.75 0.25x + x2 = -8.75 The x term is 0.25x. Take half its coefficient (0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. 0.25x + 0.015625 + x2 = -8.75 + 0.015625 Reorder the terms: 0.015625 + 0.25x + x2 = -8.75 + 0.015625 Combine like terms: -8.75 + 0.015625 = -8.734375 0.015625 + 0.25x + x2 = -8.734375 Factor a perfect square on the left side: (x + 0.125)(x + 0.125) = -8.734375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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