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Simplifying 3x2 + 16x = 264 Reorder the terms: 16x + 3x2 = 264 Solving 16x + 3x2 = 264 Solving for variable 'x'. Reorder the terms: -264 + 16x + 3x2 = 264 + -264 Combine like terms: 264 + -264 = 0 -264 + 16x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -88 + 5.333333333x + x2 = 0 Move the constant term to the right: Add '88' to each side of the equation. -88 + 5.333333333x + 88 + x2 = 0 + 88 Reorder the terms: -88 + 88 + 5.333333333x + x2 = 0 + 88 Combine like terms: -88 + 88 = 0 0 + 5.333333333x + x2 = 0 + 88 5.333333333x + x2 = 0 + 88 Combine like terms: 0 + 88 = 88 5.333333333x + x2 = 88 The x term is 5.333333333x. Take half its coefficient (2.666666667). Square it (7.111111113) and add it to both sides. Add '7.111111113' to each side of the equation. 5.333333333x + 7.111111113 + x2 = 88 + 7.111111113 Reorder the terms: 7.111111113 + 5.333333333x + x2 = 88 + 7.111111113 Combine like terms: 88 + 7.111111113 = 95.111111113 7.111111113 + 5.333333333x + x2 = 95.111111113 Factor a perfect square on the left side: (x + 2.666666667)(x + 2.666666667) = 95.111111113 Calculate the square root of the right side: 9.752492559 Break this problem into two subproblems by setting (x + 2.666666667) equal to 9.752492559 and -9.752492559.Subproblem 1
x + 2.666666667 = 9.752492559 Simplifying x + 2.666666667 = 9.752492559 Reorder the terms: 2.666666667 + x = 9.752492559 Solving 2.666666667 + x = 9.752492559 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.666666667' to each side of the equation. 2.666666667 + -2.666666667 + x = 9.752492559 + -2.666666667 Combine like terms: 2.666666667 + -2.666666667 = 0.000000000 0.000000000 + x = 9.752492559 + -2.666666667 x = 9.752492559 + -2.666666667 Combine like terms: 9.752492559 + -2.666666667 = 7.085825892 x = 7.085825892 Simplifying x = 7.085825892Subproblem 2
x + 2.666666667 = -9.752492559 Simplifying x + 2.666666667 = -9.752492559 Reorder the terms: 2.666666667 + x = -9.752492559 Solving 2.666666667 + x = -9.752492559 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.666666667' to each side of the equation. 2.666666667 + -2.666666667 + x = -9.752492559 + -2.666666667 Combine like terms: 2.666666667 + -2.666666667 = 0.000000000 0.000000000 + x = -9.752492559 + -2.666666667 x = -9.752492559 + -2.666666667 Combine like terms: -9.752492559 + -2.666666667 = -12.419159226 x = -12.419159226 Simplifying x = -12.419159226Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.085825892, -12.419159226}
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