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Simplifying 400 = (x + 2)(x)(3) Reorder the terms: 400 = (2 + x)(x)(3) Reorder the terms for easier multiplication: 400 = 3x(2 + x) 400 = (2 * 3x + x * 3x) 400 = (6x + 3x2) Solving 400 = 6x + 3x2 Solving for variable 'x'. Reorder the terms: 400 + -6x + -3x2 = 6x + -6x + 3x2 + -3x2 Combine like terms: 6x + -6x = 0 400 + -6x + -3x2 = 0 + 3x2 + -3x2 400 + -6x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 400 + -6x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -133.3333333 + 2x + x2 = 0 Move the constant term to the right: Add '133.3333333' to each side of the equation. -133.3333333 + 2x + 133.3333333 + x2 = 0 + 133.3333333 Reorder the terms: -133.3333333 + 133.3333333 + 2x + x2 = 0 + 133.3333333 Combine like terms: -133.3333333 + 133.3333333 = 0.0000000 0.0000000 + 2x + x2 = 0 + 133.3333333 2x + x2 = 0 + 133.3333333 Combine like terms: 0 + 133.3333333 = 133.3333333 2x + x2 = 133.3333333 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 = 133.3333333 + 1 Reorder the terms: 1 + 2x + x2 = 133.3333333 + 1 Combine like terms: 133.3333333 + 1 = 134.3333333 1 + 2x + x2 = 134.3333333 Factor a perfect square on the left side: (x + 1)(x + 1) = 134.3333333 Calculate the square root of the right side: 11.590225766 Break this problem into two subproblems by setting (x + 1) equal to 11.590225766 and -11.590225766.Subproblem 1
x + 1 = 11.590225766 Simplifying x + 1 = 11.590225766 Reorder the terms: 1 + x = 11.590225766 Solving 1 + x = 11.590225766 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 = 11.590225766 + -1 Combine like terms: 1 + -1 = 0 0 + x = 11.590225766 + -1 x = 11.590225766 + -1 Combine like terms: 11.590225766 + -1 = 10.590225766 x = 10.590225766 Simplifying x = 10.590225766Subproblem 2
x + 1 = -11.590225766 Simplifying x + 1 = -11.590225766 Reorder the terms: 1 + x = -11.590225766 Solving 1 + x = -11.590225766 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 = -11.590225766 + -1 Combine like terms: 1 + -1 = 0 0 + x = -11.590225766 + -1 x = -11.590225766 + -1 Combine like terms: -11.590225766 + -1 = -12.590225766 x = -12.590225766 Simplifying x = -12.590225766Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.590225766, -12.590225766}
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