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Simplifying (3x2 + 5x + -12) + -1(x2 + 4x + 9) = x2 + -3x + -30 Reorder the terms: (-12 + 5x + 3x2) + -1(x2 + 4x + 9) = x2 + -3x + -30 Remove parenthesis around (-12 + 5x + 3x2) -12 + 5x + 3x2 + -1(x2 + 4x + 9) = x2 + -3x + -30 Reorder the terms: -12 + 5x + 3x2 + -1(9 + 4x + x2) = x2 + -3x + -30 -12 + 5x + 3x2 + (9 * -1 + 4x * -1 + x2 * -1) = x2 + -3x + -30 -12 + 5x + 3x2 + (-9 + -4x + -1x2) = x2 + -3x + -30 Reorder the terms: -12 + -9 + 5x + -4x + 3x2 + -1x2 = x2 + -3x + -30 Combine like terms: -12 + -9 = -21 -21 + 5x + -4x + 3x2 + -1x2 = x2 + -3x + -30 Combine like terms: 5x + -4x = 1x -21 + 1x + 3x2 + -1x2 = x2 + -3x + -30 Combine like terms: 3x2 + -1x2 = 2x2 -21 + 1x + 2x2 = x2 + -3x + -30 Reorder the terms: -21 + 1x + 2x2 = -30 + -3x + x2 Solving -21 + 1x + 2x2 = -30 + -3x + x2 Solving for variable 'x'. Reorder the terms: -21 + 30 + 1x + 3x + 2x2 + -1x2 = -30 + -3x + x2 + 30 + 3x + -1x2 Combine like terms: -21 + 30 = 9 9 + 1x + 3x + 2x2 + -1x2 = -30 + -3x + x2 + 30 + 3x + -1x2 Combine like terms: 1x + 3x = 4x 9 + 4x + 2x2 + -1x2 = -30 + -3x + x2 + 30 + 3x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 9 + 4x + 1x2 = -30 + -3x + x2 + 30 + 3x + -1x2 Reorder the terms: 9 + 4x + 1x2 = -30 + 30 + -3x + 3x + x2 + -1x2 Combine like terms: -30 + 30 = 0 9 + 4x + 1x2 = 0 + -3x + 3x + x2 + -1x2 9 + 4x + 1x2 = -3x + 3x + x2 + -1x2 Combine like terms: -3x + 3x = 0 9 + 4x + 1x2 = 0 + x2 + -1x2 9 + 4x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 9 + 4x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + 4x + -9 + x2 = 0 + -9 Reorder the terms: 9 + -9 + 4x + x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 4x + x2 = 0 + -9 4x + x2 = 0 + -9 Combine like terms: 0 + -9 = -9 4x + x2 = -9 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 = -9 + 4 Reorder the terms: 4 + 4x + x2 = -9 + 4 Combine like terms: -9 + 4 = -5 4 + 4x + x2 = -5 Factor a perfect square on the left side: (x + 2)(x + 2) = -5 Can't calculate square root of the right side. The solution to this equation could not be determined.
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