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Simplifying 2x2 + -7x + 9 = (x + -3)(x + 1) + -3x Reorder the terms: 9 + -7x + 2x2 = (x + -3)(x + 1) + -3x Reorder the terms: 9 + -7x + 2x2 = (-3 + x)(x + 1) + -3x Reorder the terms: 9 + -7x + 2x2 = (-3 + x)(1 + x) + -3x Multiply (-3 + x) * (1 + x) 9 + -7x + 2x2 = (-3(1 + x) + x(1 + x)) + -3x 9 + -7x + 2x2 = ((1 * -3 + x * -3) + x(1 + x)) + -3x 9 + -7x + 2x2 = ((-3 + -3x) + x(1 + x)) + -3x 9 + -7x + 2x2 = (-3 + -3x + (1 * x + x * x)) + -3x 9 + -7x + 2x2 = (-3 + -3x + (1x + x2)) + -3x Combine like terms: -3x + 1x = -2x 9 + -7x + 2x2 = (-3 + -2x + x2) + -3x Reorder the terms: 9 + -7x + 2x2 = -3 + -2x + -3x + x2 Combine like terms: -2x + -3x = -5x 9 + -7x + 2x2 = -3 + -5x + x2 Solving 9 + -7x + 2x2 = -3 + -5x + x2 Solving for variable 'x'. Reorder the terms: 9 + 3 + -7x + 5x + 2x2 + -1x2 = -3 + -5x + x2 + 3 + 5x + -1x2 Combine like terms: 9 + 3 = 12 12 + -7x + 5x + 2x2 + -1x2 = -3 + -5x + x2 + 3 + 5x + -1x2 Combine like terms: -7x + 5x = -2x 12 + -2x + 2x2 + -1x2 = -3 + -5x + x2 + 3 + 5x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 12 + -2x + 1x2 = -3 + -5x + x2 + 3 + 5x + -1x2 Reorder the terms: 12 + -2x + 1x2 = -3 + 3 + -5x + 5x + x2 + -1x2 Combine like terms: -3 + 3 = 0 12 + -2x + 1x2 = 0 + -5x + 5x + x2 + -1x2 12 + -2x + 1x2 = -5x + 5x + x2 + -1x2 Combine like terms: -5x + 5x = 0 12 + -2x + 1x2 = 0 + x2 + -1x2 12 + -2x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 12 + -2x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + -2x + -12 + x2 = 0 + -12 Reorder the terms: 12 + -12 + -2x + x2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -2x + x2 = 0 + -12 -2x + x2 = 0 + -12 Combine like terms: 0 + -12 = -12 -2x + x2 = -12 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = -12 + 1 Reorder the terms: 1 + -2x + x2 = -12 + 1 Combine like terms: -12 + 1 = -11 1 + -2x + x2 = -11 Factor a perfect square on the left side: (x + -1)(x + -1) = -11 Can't calculate square root of the right side. The solution to this equation could not be determined.
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