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Simplifying (2x + -3 + x)(x + 3) = 2 Reorder the terms: (-3 + 2x + x)(x + 3) = 2 Combine like terms: 2x + x = 3x (-3 + 3x)(x + 3) = 2 Reorder the terms: (-3 + 3x)(3 + x) = 2 Multiply (-3 + 3x) * (3 + x) (-3(3 + x) + 3x * (3 + x)) = 2 ((3 * -3 + x * -3) + 3x * (3 + x)) = 2 ((-9 + -3x) + 3x * (3 + x)) = 2 (-9 + -3x + (3 * 3x + x * 3x)) = 2 (-9 + -3x + (9x + 3x2)) = 2 Combine like terms: -3x + 9x = 6x (-9 + 6x + 3x2) = 2 Solving -9 + 6x + 3x2 = 2 Solving for variable 'x'. Reorder the terms: -9 + -2 + 6x + 3x2 = 2 + -2 Combine like terms: -9 + -2 = -11 -11 + 6x + 3x2 = 2 + -2 Combine like terms: 2 + -2 = 0 -11 + 6x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -3.666666667 + 2x + x2 = 0 Move the constant term to the right: Add '3.666666667' to each side of the equation. -3.666666667 + 2x + 3.666666667 + x2 = 0 + 3.666666667 Reorder the terms: -3.666666667 + 3.666666667 + 2x + x2 = 0 + 3.666666667 Combine like terms: -3.666666667 + 3.666666667 = 0.000000000 0.000000000 + 2x + x2 = 0 + 3.666666667 2x + x2 = 0 + 3.666666667 Combine like terms: 0 + 3.666666667 = 3.666666667 2x + x2 = 3.666666667 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 = 3.666666667 + 1 Reorder the terms: 1 + 2x + x2 = 3.666666667 + 1 Combine like terms: 3.666666667 + 1 = 4.666666667 1 + 2x + x2 = 4.666666667 Factor a perfect square on the left side: (x + 1)(x + 1) = 4.666666667 Calculate the square root of the right side: 2.1602469 Break this problem into two subproblems by setting (x + 1) equal to 2.1602469 and -2.1602469.Subproblem 1
x + 1 = 2.1602469 Simplifying x + 1 = 2.1602469 Reorder the terms: 1 + x = 2.1602469 Solving 1 + x = 2.1602469 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 = 2.1602469 + -1 Combine like terms: 1 + -1 = 0 0 + x = 2.1602469 + -1 x = 2.1602469 + -1 Combine like terms: 2.1602469 + -1 = 1.1602469 x = 1.1602469 Simplifying x = 1.1602469Subproblem 2
x + 1 = -2.1602469 Simplifying x + 1 = -2.1602469 Reorder the terms: 1 + x = -2.1602469 Solving 1 + x = -2.1602469 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 = -2.1602469 + -1 Combine like terms: 1 + -1 = 0 0 + x = -2.1602469 + -1 x = -2.1602469 + -1 Combine like terms: -2.1602469 + -1 = -3.1602469 x = -3.1602469 Simplifying x = -3.1602469Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1602469, -3.1602469}
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