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Simplifying 3x2 + -84x + 26 = 0 Reorder the terms: 26 + -84x + 3x2 = 0 Solving 26 + -84x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 8.666666667 + -28x + x2 = 0 Move the constant term to the right: Add '-8.666666667' to each side of the equation. 8.666666667 + -28x + -8.666666667 + x2 = 0 + -8.666666667 Reorder the terms: 8.666666667 + -8.666666667 + -28x + x2 = 0 + -8.666666667 Combine like terms: 8.666666667 + -8.666666667 = 0.000000000 0.000000000 + -28x + x2 = 0 + -8.666666667 -28x + x2 = 0 + -8.666666667 Combine like terms: 0 + -8.666666667 = -8.666666667 -28x + x2 = -8.666666667 The x term is -28x. Take half its coefficient (-14). Square it (196) and add it to both sides. Add '196' to each side of the equation. -28x + 196 + x2 = -8.666666667 + 196 Reorder the terms: 196 + -28x + x2 = -8.666666667 + 196 Combine like terms: -8.666666667 + 196 = 187.333333333 196 + -28x + x2 = 187.333333333 Factor a perfect square on the left side: (x + -14)(x + -14) = 187.333333333 Calculate the square root of the right side: 13.686976778 Break this problem into two subproblems by setting (x + -14) equal to 13.686976778 and -13.686976778.Subproblem 1
x + -14 = 13.686976778 Simplifying x + -14 = 13.686976778 Reorder the terms: -14 + x = 13.686976778 Solving -14 + x = 13.686976778 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x = 13.686976778 + 14 Combine like terms: -14 + 14 = 0 0 + x = 13.686976778 + 14 x = 13.686976778 + 14 Combine like terms: 13.686976778 + 14 = 27.686976778 x = 27.686976778 Simplifying x = 27.686976778Subproblem 2
x + -14 = -13.686976778 Simplifying x + -14 = -13.686976778 Reorder the terms: -14 + x = -13.686976778 Solving -14 + x = -13.686976778 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x = -13.686976778 + 14 Combine like terms: -14 + 14 = 0 0 + x = -13.686976778 + 14 x = -13.686976778 + 14 Combine like terms: -13.686976778 + 14 = 0.313023222 x = 0.313023222 Simplifying x = 0.313023222Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.686976778, 0.313023222}
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