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Simplifying 5(x + -1) + -2(x2 + 5x + 6) + -7(x + 6) = 0 Reorder the terms: 5(-1 + x) + -2(x2 + 5x + 6) + -7(x + 6) = 0 (-1 * 5 + x * 5) + -2(x2 + 5x + 6) + -7(x + 6) = 0 (-5 + 5x) + -2(x2 + 5x + 6) + -7(x + 6) = 0 Reorder the terms: -5 + 5x + -2(6 + 5x + x2) + -7(x + 6) = 0 -5 + 5x + (6 * -2 + 5x * -2 + x2 * -2) + -7(x + 6) = 0 -5 + 5x + (-12 + -10x + -2x2) + -7(x + 6) = 0 Reorder the terms: -5 + 5x + -12 + -10x + -2x2 + -7(6 + x) = 0 -5 + 5x + -12 + -10x + -2x2 + (6 * -7 + x * -7) = 0 -5 + 5x + -12 + -10x + -2x2 + (-42 + -7x) = 0 Reorder the terms: -5 + -12 + -42 + 5x + -10x + -7x + -2x2 = 0 Combine like terms: -5 + -12 = -17 -17 + -42 + 5x + -10x + -7x + -2x2 = 0 Combine like terms: -17 + -42 = -59 -59 + 5x + -10x + -7x + -2x2 = 0 Combine like terms: 5x + -10x = -5x -59 + -5x + -7x + -2x2 = 0 Combine like terms: -5x + -7x = -12x -59 + -12x + -2x2 = 0 Solving -59 + -12x + -2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(59 + 12x + 2x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(59 + 12x + 2x2)' equal to zero and attempt to solve: Simplifying 59 + 12x + 2x2 = 0 Solving 59 + 12x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 29.5 + 6x + x2 = 0 Move the constant term to the right: Add '-29.5' to each side of the equation. 29.5 + 6x + -29.5 + x2 = 0 + -29.5 Reorder the terms: 29.5 + -29.5 + 6x + x2 = 0 + -29.5 Combine like terms: 29.5 + -29.5 = 0.0 0.0 + 6x + x2 = 0 + -29.5 6x + x2 = 0 + -29.5 Combine like terms: 0 + -29.5 = -29.5 6x + x2 = -29.5 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = -29.5 + 9 Reorder the terms: 9 + 6x + x2 = -29.5 + 9 Combine like terms: -29.5 + 9 = -20.5 9 + 6x + x2 = -20.5 Factor a perfect square on the left side: (x + 3)(x + 3) = -20.5 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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