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Simplifying 3x(x + -3) + 5(x + 7) + -1x(x + 1) + -2(x + 7) + 4 = 0 Reorder the terms: 3x(-3 + x) + 5(x + 7) + -1x(x + 1) + -2(x + 7) + 4 = 0 (-3 * 3x + x * 3x) + 5(x + 7) + -1x(x + 1) + -2(x + 7) + 4 = 0 (-9x + 3x2) + 5(x + 7) + -1x(x + 1) + -2(x + 7) + 4 = 0 Reorder the terms: -9x + 3x2 + 5(7 + x) + -1x(x + 1) + -2(x + 7) + 4 = 0 -9x + 3x2 + (7 * 5 + x * 5) + -1x(x + 1) + -2(x + 7) + 4 = 0 -9x + 3x2 + (35 + 5x) + -1x(x + 1) + -2(x + 7) + 4 = 0 Reorder the terms: -9x + 3x2 + 35 + 5x + -1x(1 + x) + -2(x + 7) + 4 = 0 -9x + 3x2 + 35 + 5x + (1 * -1x + x * -1x) + -2(x + 7) + 4 = 0 -9x + 3x2 + 35 + 5x + (-1x + -1x2) + -2(x + 7) + 4 = 0 Reorder the terms: -9x + 3x2 + 35 + 5x + -1x + -1x2 + -2(7 + x) + 4 = 0 -9x + 3x2 + 35 + 5x + -1x + -1x2 + (7 * -2 + x * -2) + 4 = 0 -9x + 3x2 + 35 + 5x + -1x + -1x2 + (-14 + -2x) + 4 = 0 Reorder the terms: 35 + -14 + 4 + -9x + 5x + -1x + -2x + 3x2 + -1x2 = 0 Combine like terms: 35 + -14 = 21 21 + 4 + -9x + 5x + -1x + -2x + 3x2 + -1x2 = 0 Combine like terms: 21 + 4 = 25 25 + -9x + 5x + -1x + -2x + 3x2 + -1x2 = 0 Combine like terms: -9x + 5x = -4x 25 + -4x + -1x + -2x + 3x2 + -1x2 = 0 Combine like terms: -4x + -1x = -5x 25 + -5x + -2x + 3x2 + -1x2 = 0 Combine like terms: -5x + -2x = -7x 25 + -7x + 3x2 + -1x2 = 0 Combine like terms: 3x2 + -1x2 = 2x2 25 + -7x + 2x2 = 0 Solving 25 + -7x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 12.5 + -3.5x + x2 = 0 Move the constant term to the right: Add '-12.5' to each side of the equation. 12.5 + -3.5x + -12.5 + x2 = 0 + -12.5 Reorder the terms: 12.5 + -12.5 + -3.5x + x2 = 0 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + -3.5x + x2 = 0 + -12.5 -3.5x + x2 = 0 + -12.5 Combine like terms: 0 + -12.5 = -12.5 -3.5x + x2 = -12.5 The x term is -3.5x. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5x + 3.0625 + x2 = -12.5 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = -12.5 + 3.0625 Combine like terms: -12.5 + 3.0625 = -9.4375 3.0625 + -3.5x + x2 = -9.4375 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = -9.4375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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