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Simplifying 36x2 + -43x + 9 = 0 Reorder the terms: 9 + -43x + 36x2 = 0 Solving 9 + -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'. 0.25 + -1.194444444x + x2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + -1.194444444x + -0.25 + x2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + -1.194444444x + x2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + -1.194444444x + x2 = 0 + -0.25 -1.194444444x + x2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 -1.194444444x + x2 = -0.25 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 = -0.25 + 0.3566743825 Reorder the terms: 0.3566743825 + -1.194444444x + x2 = -0.25 + 0.3566743825 Combine like terms: -0.25 + 0.3566743825 = 0.1066743825 0.3566743825 + -1.194444444x + x2 = 0.1066743825 Factor a perfect square on the left side: (x + -0.597222222)(x + -0.597222222) = 0.1066743825 Calculate the square root of the right side: 0.326610445 Break this problem into two subproblems by setting (x + -0.597222222) equal to 0.326610445 and -0.326610445.Subproblem 1
x + -0.597222222 = 0.326610445 Simplifying x + -0.597222222 = 0.326610445 Reorder the terms: -0.597222222 + x = 0.326610445 Solving -0.597222222 + x = 0.326610445 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 = 0.326610445 + 0.597222222 Combine like terms: -0.597222222 + 0.597222222 = 0.000000000 0.000000000 + x = 0.326610445 + 0.597222222 x = 0.326610445 + 0.597222222 Combine like terms: 0.326610445 + 0.597222222 = 0.923832667 x = 0.923832667 Simplifying x = 0.923832667Subproblem 2
x + -0.597222222 = -0.326610445 Simplifying x + -0.597222222 = -0.326610445 Reorder the terms: -0.597222222 + x = -0.326610445 Solving -0.597222222 + x = -0.326610445 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 = -0.326610445 + 0.597222222 Combine like terms: -0.597222222 + 0.597222222 = 0.000000000 0.000000000 + x = -0.326610445 + 0.597222222 x = -0.326610445 + 0.597222222 Combine like terms: -0.326610445 + 0.597222222 = 0.270611777 x = 0.270611777 Simplifying x = 0.270611777Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.923832667, 0.270611777}
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