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Simplifying 13 = 3(x + -1)(x + -8) Reorder the terms: 13 = 3(-1 + x)(x + -8) Reorder the terms: 13 = 3(-1 + x)(-8 + x) Multiply (-1 + x) * (-8 + x) 13 = 3(-1(-8 + x) + x(-8 + x)) 13 = 3((-8 * -1 + x * -1) + x(-8 + x)) 13 = 3((8 + -1x) + x(-8 + x)) 13 = 3(8 + -1x + (-8 * x + x * x)) 13 = 3(8 + -1x + (-8x + x2)) Combine like terms: -1x + -8x = -9x 13 = 3(8 + -9x + x2) 13 = (8 * 3 + -9x * 3 + x2 * 3) 13 = (24 + -27x + 3x2) Solving 13 = 24 + -27x + 3x2 Solving for variable 'x'. Combine like terms: 13 + -24 = -11 -11 + 27x + -3x2 = 24 + -27x + 3x2 + -24 + 27x + -3x2 Reorder the terms: -11 + 27x + -3x2 = 24 + -24 + -27x + 27x + 3x2 + -3x2 Combine like terms: 24 + -24 = 0 -11 + 27x + -3x2 = 0 + -27x + 27x + 3x2 + -3x2 -11 + 27x + -3x2 = -27x + 27x + 3x2 + -3x2 Combine like terms: -27x + 27x = 0 -11 + 27x + -3x2 = 0 + 3x2 + -3x2 -11 + 27x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -11 + 27x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 3.666666667 + -9x + x2 = 0 Move the constant term to the right: Add '-3.666666667' to each side of the equation. 3.666666667 + -9x + -3.666666667 + x2 = 0 + -3.666666667 Reorder the terms: 3.666666667 + -3.666666667 + -9x + x2 = 0 + -3.666666667 Combine like terms: 3.666666667 + -3.666666667 = 0.000000000 0.000000000 + -9x + x2 = 0 + -3.666666667 -9x + x2 = 0 + -3.666666667 Combine like terms: 0 + -3.666666667 = -3.666666667 -9x + x2 = -3.666666667 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = -3.666666667 + 20.25 Reorder the terms: 20.25 + -9x + x2 = -3.666666667 + 20.25 Combine like terms: -3.666666667 + 20.25 = 16.583333333 20.25 + -9x + x2 = 16.583333333 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 16.583333333 Calculate the square root of the right side: 4.072263908 Break this problem into two subproblems by setting (x + -4.5) equal to 4.072263908 and -4.072263908.Subproblem 1
x + -4.5 = 4.072263908 Simplifying x + -4.5 = 4.072263908 Reorder the terms: -4.5 + x = 4.072263908 Solving -4.5 + x = 4.072263908 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 4.072263908 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 4.072263908 + 4.5 x = 4.072263908 + 4.5 Combine like terms: 4.072263908 + 4.5 = 8.572263908 x = 8.572263908 Simplifying x = 8.572263908Subproblem 2
x + -4.5 = -4.072263908 Simplifying x + -4.5 = -4.072263908 Reorder the terms: -4.5 + x = -4.072263908 Solving -4.5 + x = -4.072263908 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -4.072263908 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -4.072263908 + 4.5 x = -4.072263908 + 4.5 Combine like terms: -4.072263908 + 4.5 = 0.427736092 x = 0.427736092 Simplifying x = 0.427736092Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.572263908, 0.427736092}
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