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Simplifying (x + 2) * 3x = 161 Reorder the terms: (2 + x) * 3x = 161 Reorder the terms for easier multiplication: 3x(2 + x) = 161 (2 * 3x + x * 3x) = 161 (6x + 3x2) = 161 Solving 6x + 3x2 = 161 Solving for variable 'x'. Reorder the terms: -161 + 6x + 3x2 = 161 + -161 Combine like terms: 161 + -161 = 0 -161 + 6x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -53.66666667 + 2x + x2 = 0 Move the constant term to the right: Add '53.66666667' to each side of the equation. -53.66666667 + 2x + 53.66666667 + x2 = 0 + 53.66666667 Reorder the terms: -53.66666667 + 53.66666667 + 2x + x2 = 0 + 53.66666667 Combine like terms: -53.66666667 + 53.66666667 = 0.00000000 0.00000000 + 2x + x2 = 0 + 53.66666667 2x + x2 = 0 + 53.66666667 Combine like terms: 0 + 53.66666667 = 53.66666667 2x + x2 = 53.66666667 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 = 53.66666667 + 1 Reorder the terms: 1 + 2x + x2 = 53.66666667 + 1 Combine like terms: 53.66666667 + 1 = 54.66666667 1 + 2x + x2 = 54.66666667 Factor a perfect square on the left side: (x + 1)(x + 1) = 54.66666667 Calculate the square root of the right side: 7.393691004 Break this problem into two subproblems by setting (x + 1) equal to 7.393691004 and -7.393691004.Subproblem 1
x + 1 = 7.393691004 Simplifying x + 1 = 7.393691004 Reorder the terms: 1 + x = 7.393691004 Solving 1 + x = 7.393691004 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 = 7.393691004 + -1 Combine like terms: 1 + -1 = 0 0 + x = 7.393691004 + -1 x = 7.393691004 + -1 Combine like terms: 7.393691004 + -1 = 6.393691004 x = 6.393691004 Simplifying x = 6.393691004Subproblem 2
x + 1 = -7.393691004 Simplifying x + 1 = -7.393691004 Reorder the terms: 1 + x = -7.393691004 Solving 1 + x = -7.393691004 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 = -7.393691004 + -1 Combine like terms: 1 + -1 = 0 0 + x = -7.393691004 + -1 x = -7.393691004 + -1 Combine like terms: -7.393691004 + -1 = -8.393691004 x = -8.393691004 Simplifying x = -8.393691004Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.393691004, -8.393691004}
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