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Simplifying 3x2 + -51x + 154 = 0 Reorder the terms: 154 + -51x + 3x2 = 0 Solving 154 + -51x + 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'. 51.33333333 + -17x + x2 = 0 Move the constant term to the right: Add '-51.33333333' to each side of the equation. 51.33333333 + -17x + -51.33333333 + x2 = 0 + -51.33333333 Reorder the terms: 51.33333333 + -51.33333333 + -17x + x2 = 0 + -51.33333333 Combine like terms: 51.33333333 + -51.33333333 = 0.00000000 0.00000000 + -17x + x2 = 0 + -51.33333333 -17x + x2 = 0 + -51.33333333 Combine like terms: 0 + -51.33333333 = -51.33333333 -17x + x2 = -51.33333333 The x term is -17x. Take half its coefficient (-8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. -17x + 72.25 + x2 = -51.33333333 + 72.25 Reorder the terms: 72.25 + -17x + x2 = -51.33333333 + 72.25 Combine like terms: -51.33333333 + 72.25 = 20.91666667 72.25 + -17x + x2 = 20.91666667 Factor a perfect square on the left side: (x + -8.5)(x + -8.5) = 20.91666667 Calculate the square root of the right side: 4.573474245 Break this problem into two subproblems by setting (x + -8.5) equal to 4.573474245 and -4.573474245.Subproblem 1
x + -8.5 = 4.573474245 Simplifying x + -8.5 = 4.573474245 Reorder the terms: -8.5 + x = 4.573474245 Solving -8.5 + x = 4.573474245 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = 4.573474245 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = 4.573474245 + 8.5 x = 4.573474245 + 8.5 Combine like terms: 4.573474245 + 8.5 = 13.073474245 x = 13.073474245 Simplifying x = 13.073474245Subproblem 2
x + -8.5 = -4.573474245 Simplifying x + -8.5 = -4.573474245 Reorder the terms: -8.5 + x = -4.573474245 Solving -8.5 + x = -4.573474245 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = -4.573474245 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = -4.573474245 + 8.5 x = -4.573474245 + 8.5 Combine like terms: -4.573474245 + 8.5 = 3.926525755 x = 3.926525755 Simplifying x = 3.926525755Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.073474245, 3.926525755}
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