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Simplifying 3x2 + 72x + 16 = 0 Reorder the terms: 16 + 72x + 3x2 = 0 Solving 16 + 72x + 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'. 5.333333333 + 24x + x2 = 0 Move the constant term to the right: Add '-5.333333333' to each side of the equation. 5.333333333 + 24x + -5.333333333 + x2 = 0 + -5.333333333 Reorder the terms: 5.333333333 + -5.333333333 + 24x + x2 = 0 + -5.333333333 Combine like terms: 5.333333333 + -5.333333333 = 0.000000000 0.000000000 + 24x + x2 = 0 + -5.333333333 24x + x2 = 0 + -5.333333333 Combine like terms: 0 + -5.333333333 = -5.333333333 24x + x2 = -5.333333333 The x term is 24x. Take half its coefficient (12). Square it (144) and add it to both sides. Add '144' to each side of the equation. 24x + 144 + x2 = -5.333333333 + 144 Reorder the terms: 144 + 24x + x2 = -5.333333333 + 144 Combine like terms: -5.333333333 + 144 = 138.666666667 144 + 24x + x2 = 138.666666667 Factor a perfect square on the left side: (x + 12)(x + 12) = 138.666666667 Calculate the square root of the right side: 11.775681155 Break this problem into two subproblems by setting (x + 12) equal to 11.775681155 and -11.775681155.Subproblem 1
x + 12 = 11.775681155 Simplifying x + 12 = 11.775681155 Reorder the terms: 12 + x = 11.775681155 Solving 12 + x = 11.775681155 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = 11.775681155 + -12 Combine like terms: 12 + -12 = 0 0 + x = 11.775681155 + -12 x = 11.775681155 + -12 Combine like terms: 11.775681155 + -12 = -0.224318845 x = -0.224318845 Simplifying x = -0.224318845Subproblem 2
x + 12 = -11.775681155 Simplifying x + 12 = -11.775681155 Reorder the terms: 12 + x = -11.775681155 Solving 12 + x = -11.775681155 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = -11.775681155 + -12 Combine like terms: 12 + -12 = 0 0 + x = -11.775681155 + -12 x = -11.775681155 + -12 Combine like terms: -11.775681155 + -12 = -23.775681155 x = -23.775681155 Simplifying x = -23.775681155Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.224318845, -23.775681155}
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