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Simplifying 16 = 3(x + -1)(x + -7) Reorder the terms: 16 = 3(-1 + x)(x + -7) Reorder the terms: 16 = 3(-1 + x)(-7 + x) Multiply (-1 + x) * (-7 + x) 16 = 3(-1(-7 + x) + x(-7 + x)) 16 = 3((-7 * -1 + x * -1) + x(-7 + x)) 16 = 3((7 + -1x) + x(-7 + x)) 16 = 3(7 + -1x + (-7 * x + x * x)) 16 = 3(7 + -1x + (-7x + x2)) Combine like terms: -1x + -7x = -8x 16 = 3(7 + -8x + x2) 16 = (7 * 3 + -8x * 3 + x2 * 3) 16 = (21 + -24x + 3x2) Solving 16 = 21 + -24x + 3x2 Solving for variable 'x'. Combine like terms: 16 + -21 = -5 -5 + 24x + -3x2 = 21 + -24x + 3x2 + -21 + 24x + -3x2 Reorder the terms: -5 + 24x + -3x2 = 21 + -21 + -24x + 24x + 3x2 + -3x2 Combine like terms: 21 + -21 = 0 -5 + 24x + -3x2 = 0 + -24x + 24x + 3x2 + -3x2 -5 + 24x + -3x2 = -24x + 24x + 3x2 + -3x2 Combine like terms: -24x + 24x = 0 -5 + 24x + -3x2 = 0 + 3x2 + -3x2 -5 + 24x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -5 + 24x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 1.666666667 + -8x + x2 = 0 Move the constant term to the right: Add '-1.666666667' to each side of the equation. 1.666666667 + -8x + -1.666666667 + x2 = 0 + -1.666666667 Reorder the terms: 1.666666667 + -1.666666667 + -8x + x2 = 0 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + -8x + x2 = 0 + -1.666666667 -8x + x2 = 0 + -1.666666667 Combine like terms: 0 + -1.666666667 = -1.666666667 -8x + x2 = -1.666666667 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = -1.666666667 + 16 Reorder the terms: 16 + -8x + x2 = -1.666666667 + 16 Combine like terms: -1.666666667 + 16 = 14.333333333 16 + -8x + x2 = 14.333333333 Factor a perfect square on the left side: (x + -4)(x + -4) = 14.333333333 Calculate the square root of the right side: 3.785938897 Break this problem into two subproblems by setting (x + -4) equal to 3.785938897 and -3.785938897.Subproblem 1
x + -4 = 3.785938897 Simplifying x + -4 = 3.785938897 Reorder the terms: -4 + x = 3.785938897 Solving -4 + x = 3.785938897 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 3.785938897 + 4 Combine like terms: -4 + 4 = 0 0 + x = 3.785938897 + 4 x = 3.785938897 + 4 Combine like terms: 3.785938897 + 4 = 7.785938897 x = 7.785938897 Simplifying x = 7.785938897Subproblem 2
x + -4 = -3.785938897 Simplifying x + -4 = -3.785938897 Reorder the terms: -4 + x = -3.785938897 Solving -4 + x = -3.785938897 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -3.785938897 + 4 Combine like terms: -4 + 4 = 0 0 + x = -3.785938897 + 4 x = -3.785938897 + 4 Combine like terms: -3.785938897 + 4 = 0.214061103 x = 0.214061103 Simplifying x = 0.214061103Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.785938897, 0.214061103}
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