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Simplifying 3x2 + -84x + 50 = 0 Reorder the terms: 50 + -84x + 3x2 = 0 Solving 50 + -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'. 16.66666667 + -28x + x2 = 0 Move the constant term to the right: Add '-16.66666667' to each side of the equation. 16.66666667 + -28x + -16.66666667 + x2 = 0 + -16.66666667 Reorder the terms: 16.66666667 + -16.66666667 + -28x + x2 = 0 + -16.66666667 Combine like terms: 16.66666667 + -16.66666667 = 0.00000000 0.00000000 + -28x + x2 = 0 + -16.66666667 -28x + x2 = 0 + -16.66666667 Combine like terms: 0 + -16.66666667 = -16.66666667 -28x + x2 = -16.66666667 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 = -16.66666667 + 196 Reorder the terms: 196 + -28x + x2 = -16.66666667 + 196 Combine like terms: -16.66666667 + 196 = 179.33333333 196 + -28x + x2 = 179.33333333 Factor a perfect square on the left side: (x + -14)(x + -14) = 179.33333333 Calculate the square root of the right side: 13.391539618 Break this problem into two subproblems by setting (x + -14) equal to 13.391539618 and -13.391539618.Subproblem 1
x + -14 = 13.391539618 Simplifying x + -14 = 13.391539618 Reorder the terms: -14 + x = 13.391539618 Solving -14 + x = 13.391539618 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 = 13.391539618 + 14 Combine like terms: -14 + 14 = 0 0 + x = 13.391539618 + 14 x = 13.391539618 + 14 Combine like terms: 13.391539618 + 14 = 27.391539618 x = 27.391539618 Simplifying x = 27.391539618Subproblem 2
x + -14 = -13.391539618 Simplifying x + -14 = -13.391539618 Reorder the terms: -14 + x = -13.391539618 Solving -14 + x = -13.391539618 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 = -13.391539618 + 14 Combine like terms: -14 + 14 = 0 0 + x = -13.391539618 + 14 x = -13.391539618 + 14 Combine like terms: -13.391539618 + 14 = 0.608460382 x = 0.608460382 Simplifying x = 0.608460382Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.391539618, 0.608460382}
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