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Simplifying 3x2 + 6x + -3 = 19 Reorder the terms: -3 + 6x + 3x2 = 19 Solving -3 + 6x + 3x2 = 19 Solving for variable 'x'. Reorder the terms: -3 + -19 + 6x + 3x2 = 19 + -19 Combine like terms: -3 + -19 = -22 -22 + 6x + 3x2 = 19 + -19 Combine like terms: 19 + -19 = 0 -22 + 6x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -7.333333333 + 2x + x2 = 0 Move the constant term to the right: Add '7.333333333' to each side of the equation. -7.333333333 + 2x + 7.333333333 + x2 = 0 + 7.333333333 Reorder the terms: -7.333333333 + 7.333333333 + 2x + x2 = 0 + 7.333333333 Combine like terms: -7.333333333 + 7.333333333 = 0.000000000 0.000000000 + 2x + x2 = 0 + 7.333333333 2x + x2 = 0 + 7.333333333 Combine like terms: 0 + 7.333333333 = 7.333333333 2x + x2 = 7.333333333 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 = 7.333333333 + 1 Reorder the terms: 1 + 2x + x2 = 7.333333333 + 1 Combine like terms: 7.333333333 + 1 = 8.333333333 1 + 2x + x2 = 8.333333333 Factor a perfect square on the left side: (x + 1)(x + 1) = 8.333333333 Calculate the square root of the right side: 2.886751346 Break this problem into two subproblems by setting (x + 1) equal to 2.886751346 and -2.886751346.Subproblem 1
x + 1 = 2.886751346 Simplifying x + 1 = 2.886751346 Reorder the terms: 1 + x = 2.886751346 Solving 1 + x = 2.886751346 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 = 2.886751346 + -1 Combine like terms: 1 + -1 = 0 0 + x = 2.886751346 + -1 x = 2.886751346 + -1 Combine like terms: 2.886751346 + -1 = 1.886751346 x = 1.886751346 Simplifying x = 1.886751346Subproblem 2
x + 1 = -2.886751346 Simplifying x + 1 = -2.886751346 Reorder the terms: 1 + x = -2.886751346 Solving 1 + x = -2.886751346 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 = -2.886751346 + -1 Combine like terms: 1 + -1 = 0 0 + x = -2.886751346 + -1 x = -2.886751346 + -1 Combine like terms: -2.886751346 + -1 = -3.886751346 x = -3.886751346 Simplifying x = -3.886751346Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.886751346, -3.886751346}
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