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Simplifying 144x2 + 72x + -11 = 0 Reorder the terms: -11 + 72x + 144x2 = 0 Solving -11 + 72x + 144x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 144 the coefficient of the squared term: Divide each side by '144'. -0.07638888889 + 0.5x + x2 = 0 Move the constant term to the right: Add '0.07638888889' to each side of the equation. -0.07638888889 + 0.5x + 0.07638888889 + x2 = 0 + 0.07638888889 Reorder the terms: -0.07638888889 + 0.07638888889 + 0.5x + x2 = 0 + 0.07638888889 Combine like terms: -0.07638888889 + 0.07638888889 = 0.00000000000 0.00000000000 + 0.5x + x2 = 0 + 0.07638888889 0.5x + x2 = 0 + 0.07638888889 Combine like terms: 0 + 0.07638888889 = 0.07638888889 0.5x + x2 = 0.07638888889 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 0.07638888889 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 0.07638888889 + 0.0625 Combine like terms: 0.07638888889 + 0.0625 = 0.13888888889 0.0625 + 0.5x + x2 = 0.13888888889 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 0.13888888889 Calculate the square root of the right side: 0.372677996 Break this problem into two subproblems by setting (x + 0.25) equal to 0.372677996 and -0.372677996.Subproblem 1
x + 0.25 = 0.372677996 Simplifying x + 0.25 = 0.372677996 Reorder the terms: 0.25 + x = 0.372677996 Solving 0.25 + x = 0.372677996 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 0.372677996 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 0.372677996 + -0.25 x = 0.372677996 + -0.25 Combine like terms: 0.372677996 + -0.25 = 0.122677996 x = 0.122677996 Simplifying x = 0.122677996Subproblem 2
x + 0.25 = -0.372677996 Simplifying x + 0.25 = -0.372677996 Reorder the terms: 0.25 + x = -0.372677996 Solving 0.25 + x = -0.372677996 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -0.372677996 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -0.372677996 + -0.25 x = -0.372677996 + -0.25 Combine like terms: -0.372677996 + -0.25 = -0.622677996 x = -0.622677996 Simplifying x = -0.622677996Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.122677996, -0.622677996}
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