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Simplifying 3x2 + 16x + -144 = 0 Reorder the terms: -144 + 16x + 3x2 = 0 Solving -144 + 16x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -48 + 5.333333333x + x2 = 0 Move the constant term to the right: Add '48' to each side of the equation. -48 + 5.333333333x + 48 + x2 = 0 + 48 Reorder the terms: -48 + 48 + 5.333333333x + x2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + 5.333333333x + x2 = 0 + 48 5.333333333x + x2 = 0 + 48 Combine like terms: 0 + 48 = 48 5.333333333x + x2 = 48 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 = 48 + 7.111111113 Reorder the terms: 7.111111113 + 5.333333333x + x2 = 48 + 7.111111113 Combine like terms: 48 + 7.111111113 = 55.111111113 7.111111113 + 5.333333333x + x2 = 55.111111113 Factor a perfect square on the left side: (x + 2.666666667)(x + 2.666666667) = 55.111111113 Calculate the square root of the right side: 7.423685817 Break this problem into two subproblems by setting (x + 2.666666667) equal to 7.423685817 and -7.423685817.Subproblem 1
x + 2.666666667 = 7.423685817 Simplifying x + 2.666666667 = 7.423685817 Reorder the terms: 2.666666667 + x = 7.423685817 Solving 2.666666667 + x = 7.423685817 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 = 7.423685817 + -2.666666667 Combine like terms: 2.666666667 + -2.666666667 = 0.000000000 0.000000000 + x = 7.423685817 + -2.666666667 x = 7.423685817 + -2.666666667 Combine like terms: 7.423685817 + -2.666666667 = 4.75701915 x = 4.75701915 Simplifying x = 4.75701915Subproblem 2
x + 2.666666667 = -7.423685817 Simplifying x + 2.666666667 = -7.423685817 Reorder the terms: 2.666666667 + x = -7.423685817 Solving 2.666666667 + x = -7.423685817 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 = -7.423685817 + -2.666666667 Combine like terms: 2.666666667 + -2.666666667 = 0.000000000 0.000000000 + x = -7.423685817 + -2.666666667 x = -7.423685817 + -2.666666667 Combine like terms: -7.423685817 + -2.666666667 = -10.090352484 x = -10.090352484 Simplifying x = -10.090352484Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.75701915, -10.090352484}
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