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Simplifying 5(x + -1) + -4(x2 + 3x + 4) + -9(x + 9) = 0 Reorder the terms: 5(-1 + x) + -4(x2 + 3x + 4) + -9(x + 9) = 0 (-1 * 5 + x * 5) + -4(x2 + 3x + 4) + -9(x + 9) = 0 (-5 + 5x) + -4(x2 + 3x + 4) + -9(x + 9) = 0 Reorder the terms: -5 + 5x + -4(4 + 3x + x2) + -9(x + 9) = 0 -5 + 5x + (4 * -4 + 3x * -4 + x2 * -4) + -9(x + 9) = 0 -5 + 5x + (-16 + -12x + -4x2) + -9(x + 9) = 0 Reorder the terms: -5 + 5x + -16 + -12x + -4x2 + -9(9 + x) = 0 -5 + 5x + -16 + -12x + -4x2 + (9 * -9 + x * -9) = 0 -5 + 5x + -16 + -12x + -4x2 + (-81 + -9x) = 0 Reorder the terms: -5 + -16 + -81 + 5x + -12x + -9x + -4x2 = 0 Combine like terms: -5 + -16 = -21 -21 + -81 + 5x + -12x + -9x + -4x2 = 0 Combine like terms: -21 + -81 = -102 -102 + 5x + -12x + -9x + -4x2 = 0 Combine like terms: 5x + -12x = -7x -102 + -7x + -9x + -4x2 = 0 Combine like terms: -7x + -9x = -16x -102 + -16x + -4x2 = 0 Solving -102 + -16x + -4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-2'. -2(51 + 8x + 2x2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(51 + 8x + 2x2)' equal to zero and attempt to solve: Simplifying 51 + 8x + 2x2 = 0 Solving 51 + 8x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 25.5 + 4x + x2 = 0 Move the constant term to the right: Add '-25.5' to each side of the equation. 25.5 + 4x + -25.5 + x2 = 0 + -25.5 Reorder the terms: 25.5 + -25.5 + 4x + x2 = 0 + -25.5 Combine like terms: 25.5 + -25.5 = 0.0 0.0 + 4x + x2 = 0 + -25.5 4x + x2 = 0 + -25.5 Combine like terms: 0 + -25.5 = -25.5 4x + x2 = -25.5 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 = -25.5 + 4 Reorder the terms: 4 + 4x + x2 = -25.5 + 4 Combine like terms: -25.5 + 4 = -21.5 4 + 4x + x2 = -21.5 Factor a perfect square on the left side: (x + 2)(x + 2) = -21.5 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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