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Simplifying 14x2 + -67x + 12 = 0 Reorder the terms: 12 + -67x + 14x2 = 0 Solving 12 + -67x + 14x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. 0.8571428571 + -4.785714286x + x2 = 0 Move the constant term to the right: Add '-0.8571428571' to each side of the equation. 0.8571428571 + -4.785714286x + -0.8571428571 + x2 = 0 + -0.8571428571 Reorder the terms: 0.8571428571 + -0.8571428571 + -4.785714286x + x2 = 0 + -0.8571428571 Combine like terms: 0.8571428571 + -0.8571428571 = 0.0000000000 0.0000000000 + -4.785714286x + x2 = 0 + -0.8571428571 -4.785714286x + x2 = 0 + -0.8571428571 Combine like terms: 0 + -0.8571428571 = -0.8571428571 -4.785714286x + x2 = -0.8571428571 The x term is -4.785714286x. Take half its coefficient (-2.392857143). Square it (5.725765307) and add it to both sides. Add '5.725765307' to each side of the equation. -4.785714286x + 5.725765307 + x2 = -0.8571428571 + 5.725765307 Reorder the terms: 5.725765307 + -4.785714286x + x2 = -0.8571428571 + 5.725765307 Combine like terms: -0.8571428571 + 5.725765307 = 4.8686224499 5.725765307 + -4.785714286x + x2 = 4.8686224499 Factor a perfect square on the left side: (x + -2.392857143)(x + -2.392857143) = 4.8686224499 Calculate the square root of the right side: 2.206495513 Break this problem into two subproblems by setting (x + -2.392857143) equal to 2.206495513 and -2.206495513.Subproblem 1
x + -2.392857143 = 2.206495513 Simplifying x + -2.392857143 = 2.206495513 Reorder the terms: -2.392857143 + x = 2.206495513 Solving -2.392857143 + x = 2.206495513 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.392857143' to each side of the equation. -2.392857143 + 2.392857143 + x = 2.206495513 + 2.392857143 Combine like terms: -2.392857143 + 2.392857143 = 0.000000000 0.000000000 + x = 2.206495513 + 2.392857143 x = 2.206495513 + 2.392857143 Combine like terms: 2.206495513 + 2.392857143 = 4.599352656 x = 4.599352656 Simplifying x = 4.599352656Subproblem 2
x + -2.392857143 = -2.206495513 Simplifying x + -2.392857143 = -2.206495513 Reorder the terms: -2.392857143 + x = -2.206495513 Solving -2.392857143 + x = -2.206495513 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.392857143' to each side of the equation. -2.392857143 + 2.392857143 + x = -2.206495513 + 2.392857143 Combine like terms: -2.392857143 + 2.392857143 = 0.000000000 0.000000000 + x = -2.206495513 + 2.392857143 x = -2.206495513 + 2.392857143 Combine like terms: -2.206495513 + 2.392857143 = 0.18636163 x = 0.18636163 Simplifying x = 0.18636163Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.599352656, 0.18636163}
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