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Simplifying 6x * 6x + -43x + -40 = 0 Reorder the terms for easier multiplication: 6 * 6x * x + -43x + -40 = 0 Multiply 6 * 6 36x * x + -43x + -40 = 0 Multiply x * x 36x2 + -43x + -40 = 0 Reorder the terms: -40 + -43x + 36x2 = 0 Solving -40 + -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'. -1.111111111 + -1.194444444x + x2 = 0 Move the constant term to the right: Add '1.111111111' to each side of the equation. -1.111111111 + -1.194444444x + 1.111111111 + x2 = 0 + 1.111111111 Reorder the terms: -1.111111111 + 1.111111111 + -1.194444444x + x2 = 0 + 1.111111111 Combine like terms: -1.111111111 + 1.111111111 = 0.000000000 0.000000000 + -1.194444444x + x2 = 0 + 1.111111111 -1.194444444x + x2 = 0 + 1.111111111 Combine like terms: 0 + 1.111111111 = 1.111111111 -1.194444444x + x2 = 1.111111111 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 = 1.111111111 + 0.3566743825 Reorder the terms: 0.3566743825 + -1.194444444x + x2 = 1.111111111 + 0.3566743825 Combine like terms: 1.111111111 + 0.3566743825 = 1.4677854935 0.3566743825 + -1.194444444x + x2 = 1.4677854935 Factor a perfect square on the left side: (x + -0.597222222)(x + -0.597222222) = 1.4677854935 Calculate the square root of the right side: 1.211521974 Break this problem into two subproblems by setting (x + -0.597222222) equal to 1.211521974 and -1.211521974.Subproblem 1
x + -0.597222222 = 1.211521974 Simplifying x + -0.597222222 = 1.211521974 Reorder the terms: -0.597222222 + x = 1.211521974 Solving -0.597222222 + x = 1.211521974 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 = 1.211521974 + 0.597222222 Combine like terms: -0.597222222 + 0.597222222 = 0.000000000 0.000000000 + x = 1.211521974 + 0.597222222 x = 1.211521974 + 0.597222222 Combine like terms: 1.211521974 + 0.597222222 = 1.808744196 x = 1.808744196 Simplifying x = 1.808744196Subproblem 2
x + -0.597222222 = -1.211521974 Simplifying x + -0.597222222 = -1.211521974 Reorder the terms: -0.597222222 + x = -1.211521974 Solving -0.597222222 + x = -1.211521974 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 = -1.211521974 + 0.597222222 Combine like terms: -0.597222222 + 0.597222222 = 0.000000000 0.000000000 + x = -1.211521974 + 0.597222222 x = -1.211521974 + 0.597222222 Combine like terms: -1.211521974 + 0.597222222 = -0.614299752 x = -0.614299752 Simplifying x = -0.614299752Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.808744196, -0.614299752}
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