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Simplifying 3(x + -4)(x + -9) = 122 Reorder the terms: 3(-4 + x)(x + -9) = 122 Reorder the terms: 3(-4 + x)(-9 + x) = 122 Multiply (-4 + x) * (-9 + x) 3(-4(-9 + x) + x(-9 + x)) = 122 3((-9 * -4 + x * -4) + x(-9 + x)) = 122 3((36 + -4x) + x(-9 + x)) = 122 3(36 + -4x + (-9 * x + x * x)) = 122 3(36 + -4x + (-9x + x2)) = 122 Combine like terms: -4x + -9x = -13x 3(36 + -13x + x2) = 122 (36 * 3 + -13x * 3 + x2 * 3) = 122 (108 + -39x + 3x2) = 122 Solving 108 + -39x + 3x2 = 122 Solving for variable 'x'. Reorder the terms: 108 + -122 + -39x + 3x2 = 122 + -122 Combine like terms: 108 + -122 = -14 -14 + -39x + 3x2 = 122 + -122 Combine like terms: 122 + -122 = 0 -14 + -39x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -4.666666667 + -13x + x2 = 0 Move the constant term to the right: Add '4.666666667' to each side of the equation. -4.666666667 + -13x + 4.666666667 + x2 = 0 + 4.666666667 Reorder the terms: -4.666666667 + 4.666666667 + -13x + x2 = 0 + 4.666666667 Combine like terms: -4.666666667 + 4.666666667 = 0.000000000 0.000000000 + -13x + x2 = 0 + 4.666666667 -13x + x2 = 0 + 4.666666667 Combine like terms: 0 + 4.666666667 = 4.666666667 -13x + x2 = 4.666666667 The x term is -13x. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13x + 42.25 + x2 = 4.666666667 + 42.25 Reorder the terms: 42.25 + -13x + x2 = 4.666666667 + 42.25 Combine like terms: 4.666666667 + 42.25 = 46.916666667 42.25 + -13x + x2 = 46.916666667 Factor a perfect square on the left side: (x + -6.5)(x + -6.5) = 46.916666667 Calculate the square root of the right side: 6.849574196 Break this problem into two subproblems by setting (x + -6.5) equal to 6.849574196 and -6.849574196.Subproblem 1
x + -6.5 = 6.849574196 Simplifying x + -6.5 = 6.849574196 Reorder the terms: -6.5 + x = 6.849574196 Solving -6.5 + x = 6.849574196 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = 6.849574196 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 6.849574196 + 6.5 x = 6.849574196 + 6.5 Combine like terms: 6.849574196 + 6.5 = 13.349574196 x = 13.349574196 Simplifying x = 13.349574196Subproblem 2
x + -6.5 = -6.849574196 Simplifying x + -6.5 = -6.849574196 Reorder the terms: -6.5 + x = -6.849574196 Solving -6.5 + x = -6.849574196 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = -6.849574196 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -6.849574196 + 6.5 x = -6.849574196 + 6.5 Combine like terms: -6.849574196 + 6.5 = -0.349574196 x = -0.349574196 Simplifying x = -0.349574196Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.349574196, -0.349574196}
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