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Simplifying 36x2 + 43x + -12 = 0 Reorder the terms: -12 + 43x + 36x2 = 0 Solving -12 + 43x + 36x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. -0.3333333333 + 1.194444444x + x2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + 1.194444444x + 0.3333333333 + x2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + 1.194444444x + x2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + 1.194444444x + x2 = 0 + 0.3333333333 1.194444444x + x2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 1.194444444x + x2 = 0.3333333333 The x term is 1.194444444x. Take half its coefficient (0.597222222). Square it (0.3566743825) and add it to both sides. Add '0.3566743825' to each side of the equation. 1.194444444x + 0.3566743825 + x2 = 0.3333333333 + 0.3566743825 Reorder the terms: 0.3566743825 + 1.194444444x + x2 = 0.3333333333 + 0.3566743825 Combine like terms: 0.3333333333 + 0.3566743825 = 0.6900077158 0.3566743825 + 1.194444444x + x2 = 0.6900077158 Factor a perfect square on the left side: (x + 0.597222222)(x + 0.597222222) = 0.6900077158 Calculate the square root of the right side: 0.830667031 Break this problem into two subproblems by setting (x + 0.597222222) equal to 0.830667031 and -0.830667031.Subproblem 1
x + 0.597222222 = 0.830667031 Simplifying x + 0.597222222 = 0.830667031 Reorder the terms: 0.597222222 + x = 0.830667031 Solving 0.597222222 + x = 0.830667031 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.597222222' to each side of the equation. 0.597222222 + -0.597222222 + x = 0.830667031 + -0.597222222 Combine like terms: 0.597222222 + -0.597222222 = 0.000000000 0.000000000 + x = 0.830667031 + -0.597222222 x = 0.830667031 + -0.597222222 Combine like terms: 0.830667031 + -0.597222222 = 0.233444809 x = 0.233444809 Simplifying x = 0.233444809Subproblem 2
x + 0.597222222 = -0.830667031 Simplifying x + 0.597222222 = -0.830667031 Reorder the terms: 0.597222222 + x = -0.830667031 Solving 0.597222222 + x = -0.830667031 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.597222222' to each side of the equation. 0.597222222 + -0.597222222 + x = -0.830667031 + -0.597222222 Combine like terms: 0.597222222 + -0.597222222 = 0.000000000 0.000000000 + x = -0.830667031 + -0.597222222 x = -0.830667031 + -0.597222222 Combine like terms: -0.830667031 + -0.597222222 = -1.427889253 x = -1.427889253 Simplifying x = -1.427889253Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.233444809, -1.427889253}
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