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Simplifying 3x2 + -6x + -19 = 19 Reorder the terms: -19 + -6x + 3x2 = 19 Solving -19 + -6x + 3x2 = 19 Solving for variable 'x'. Reorder the terms: -19 + -19 + -6x + 3x2 = 19 + -19 Combine like terms: -19 + -19 = -38 -38 + -6x + 3x2 = 19 + -19 Combine like terms: 19 + -19 = 0 -38 + -6x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -12.66666667 + -2x + x2 = 0 Move the constant term to the right: Add '12.66666667' to each side of the equation. -12.66666667 + -2x + 12.66666667 + x2 = 0 + 12.66666667 Reorder the terms: -12.66666667 + 12.66666667 + -2x + x2 = 0 + 12.66666667 Combine like terms: -12.66666667 + 12.66666667 = 0.00000000 0.00000000 + -2x + x2 = 0 + 12.66666667 -2x + x2 = 0 + 12.66666667 Combine like terms: 0 + 12.66666667 = 12.66666667 -2x + x2 = 12.66666667 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 12.66666667 + 1 Reorder the terms: 1 + -2x + x2 = 12.66666667 + 1 Combine like terms: 12.66666667 + 1 = 13.66666667 1 + -2x + x2 = 13.66666667 Factor a perfect square on the left side: (x + -1)(x + -1) = 13.66666667 Calculate the square root of the right side: 3.696845503 Break this problem into two subproblems by setting (x + -1) equal to 3.696845503 and -3.696845503.Subproblem 1
x + -1 = 3.696845503 Simplifying x + -1 = 3.696845503 Reorder the terms: -1 + x = 3.696845503 Solving -1 + x = 3.696845503 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 3.696845503 + 1 Combine like terms: -1 + 1 = 0 0 + x = 3.696845503 + 1 x = 3.696845503 + 1 Combine like terms: 3.696845503 + 1 = 4.696845503 x = 4.696845503 Simplifying x = 4.696845503Subproblem 2
x + -1 = -3.696845503 Simplifying x + -1 = -3.696845503 Reorder the terms: -1 + x = -3.696845503 Solving -1 + x = -3.696845503 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -3.696845503 + 1 Combine like terms: -1 + 1 = 0 0 + x = -3.696845503 + 1 x = -3.696845503 + 1 Combine like terms: -3.696845503 + 1 = -2.696845503 x = -2.696845503 Simplifying x = -2.696845503Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.696845503, -2.696845503}
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