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Simplifying x2 + 4x + -432 = 0 Reorder the terms: -432 + 4x + x2 = 0 Solving -432 + 4x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '432' to each side of the equation. -432 + 4x + 432 + x2 = 0 + 432 Reorder the terms: -432 + 432 + 4x + x2 = 0 + 432 Combine like terms: -432 + 432 = 0 0 + 4x + x2 = 0 + 432 4x + x2 = 0 + 432 Combine like terms: 0 + 432 = 432 4x + x2 = 432 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 432 + 4 Reorder the terms: 4 + 4x + x2 = 432 + 4 Combine like terms: 432 + 4 = 436 4 + 4x + x2 = 436 Factor a perfect square on the left side: (x + 2)(x + 2) = 436 Calculate the square root of the right side: 20.880613018 Break this problem into two subproblems by setting (x + 2) equal to 20.880613018 and -20.880613018.Subproblem 1
x + 2 = 20.880613018 Simplifying x + 2 = 20.880613018 Reorder the terms: 2 + x = 20.880613018 Solving 2 + x = 20.880613018 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 20.880613018 + -2 Combine like terms: 2 + -2 = 0 0 + x = 20.880613018 + -2 x = 20.880613018 + -2 Combine like terms: 20.880613018 + -2 = 18.880613018 x = 18.880613018 Simplifying x = 18.880613018Subproblem 2
x + 2 = -20.880613018 Simplifying x + 2 = -20.880613018 Reorder the terms: 2 + x = -20.880613018 Solving 2 + x = -20.880613018 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -20.880613018 + -2 Combine like terms: 2 + -2 = 0 0 + x = -20.880613018 + -2 x = -20.880613018 + -2 Combine like terms: -20.880613018 + -2 = -22.880613018 x = -22.880613018 Simplifying x = -22.880613018Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.880613018, -22.880613018}
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