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Simplifying 4x(x + 3) + 2x2 = 329 Reorder the terms: 4x(3 + x) + 2x2 = 329 (3 * 4x + x * 4x) + 2x2 = 329 (12x + 4x2) + 2x2 = 329 Combine like terms: 4x2 + 2x2 = 6x2 12x + 6x2 = 329 Solving 12x + 6x2 = 329 Solving for variable 'x'. Reorder the terms: -329 + 12x + 6x2 = 329 + -329 Combine like terms: 329 + -329 = 0 -329 + 12x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -54.83333333 + 2x + x2 = 0 Move the constant term to the right: Add '54.83333333' to each side of the equation. -54.83333333 + 2x + 54.83333333 + x2 = 0 + 54.83333333 Reorder the terms: -54.83333333 + 54.83333333 + 2x + x2 = 0 + 54.83333333 Combine like terms: -54.83333333 + 54.83333333 = 0.00000000 0.00000000 + 2x + x2 = 0 + 54.83333333 2x + x2 = 0 + 54.83333333 Combine like terms: 0 + 54.83333333 = 54.83333333 2x + x2 = 54.83333333 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 = 54.83333333 + 1 Reorder the terms: 1 + 2x + x2 = 54.83333333 + 1 Combine like terms: 54.83333333 + 1 = 55.83333333 1 + 2x + x2 = 55.83333333 Factor a perfect square on the left side: (x + 1)(x + 1) = 55.83333333 Calculate the square root of the right side: 7.47217059 Break this problem into two subproblems by setting (x + 1) equal to 7.47217059 and -7.47217059.Subproblem 1
x + 1 = 7.47217059 Simplifying x + 1 = 7.47217059 Reorder the terms: 1 + x = 7.47217059 Solving 1 + x = 7.47217059 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 = 7.47217059 + -1 Combine like terms: 1 + -1 = 0 0 + x = 7.47217059 + -1 x = 7.47217059 + -1 Combine like terms: 7.47217059 + -1 = 6.47217059 x = 6.47217059 Simplifying x = 6.47217059Subproblem 2
x + 1 = -7.47217059 Simplifying x + 1 = -7.47217059 Reorder the terms: 1 + x = -7.47217059 Solving 1 + x = -7.47217059 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 = -7.47217059 + -1 Combine like terms: 1 + -1 = 0 0 + x = -7.47217059 + -1 x = -7.47217059 + -1 Combine like terms: -7.47217059 + -1 = -8.47217059 x = -8.47217059 Simplifying x = -8.47217059Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.47217059, -8.47217059}
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