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Simplifying 0.12x2 + -0.72x + -0.137 = 0 Reorder the terms: -0.137 + -0.72x + 0.12x2 = 0 Solving -0.137 + -0.72x + 0.12x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.12 the coefficient of the squared term: Divide each side by '0.12'. -1.141666667 + -6x + x2 = 0 Move the constant term to the right: Add '1.141666667' to each side of the equation. -1.141666667 + -6x + 1.141666667 + x2 = 0 + 1.141666667 Reorder the terms: -1.141666667 + 1.141666667 + -6x + x2 = 0 + 1.141666667 Combine like terms: -1.141666667 + 1.141666667 = 0.000000000 0.000000000 + -6x + x2 = 0 + 1.141666667 -6x + x2 = 0 + 1.141666667 Combine like terms: 0 + 1.141666667 = 1.141666667 -6x + x2 = 1.141666667 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 1.141666667 + 9 Reorder the terms: 9 + -6x + x2 = 1.141666667 + 9 Combine like terms: 1.141666667 + 9 = 10.141666667 9 + -6x + x2 = 10.141666667 Factor a perfect square on the left side: (x + -3)(x + -3) = 10.141666667 Calculate the square root of the right side: 3.184598353 Break this problem into two subproblems by setting (x + -3) equal to 3.184598353 and -3.184598353.Subproblem 1
x + -3 = 3.184598353 Simplifying x + -3 = 3.184598353 Reorder the terms: -3 + x = 3.184598353 Solving -3 + x = 3.184598353 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 3.184598353 + 3 Combine like terms: -3 + 3 = 0 0 + x = 3.184598353 + 3 x = 3.184598353 + 3 Combine like terms: 3.184598353 + 3 = 6.184598353 x = 6.184598353 Simplifying x = 6.184598353Subproblem 2
x + -3 = -3.184598353 Simplifying x + -3 = -3.184598353 Reorder the terms: -3 + x = -3.184598353 Solving -3 + x = -3.184598353 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -3.184598353 + 3 Combine like terms: -3 + 3 = 0 0 + x = -3.184598353 + 3 x = -3.184598353 + 3 Combine like terms: -3.184598353 + 3 = -0.184598353 x = -0.184598353 Simplifying x = -0.184598353Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.184598353, -0.184598353}
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