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Simplifying x2 + 6x + -400 = 0 Reorder the terms: -400 + 6x + x2 = 0 Solving -400 + 6x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '400' to each side of the equation. -400 + 6x + 400 + x2 = 0 + 400 Reorder the terms: -400 + 400 + 6x + x2 = 0 + 400 Combine like terms: -400 + 400 = 0 0 + 6x + x2 = 0 + 400 6x + x2 = 0 + 400 Combine like terms: 0 + 400 = 400 6x + x2 = 400 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 400 + 9 Reorder the terms: 9 + 6x + x2 = 400 + 9 Combine like terms: 400 + 9 = 409 9 + 6x + x2 = 409 Factor a perfect square on the left side: (x + 3)(x + 3) = 409 Calculate the square root of the right side: 20.223748416 Break this problem into two subproblems by setting (x + 3) equal to 20.223748416 and -20.223748416.Subproblem 1
x + 3 = 20.223748416 Simplifying x + 3 = 20.223748416 Reorder the terms: 3 + x = 20.223748416 Solving 3 + x = 20.223748416 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 20.223748416 + -3 Combine like terms: 3 + -3 = 0 0 + x = 20.223748416 + -3 x = 20.223748416 + -3 Combine like terms: 20.223748416 + -3 = 17.223748416 x = 17.223748416 Simplifying x = 17.223748416Subproblem 2
x + 3 = -20.223748416 Simplifying x + 3 = -20.223748416 Reorder the terms: 3 + x = -20.223748416 Solving 3 + x = -20.223748416 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -20.223748416 + -3 Combine like terms: 3 + -3 = 0 0 + x = -20.223748416 + -3 x = -20.223748416 + -3 Combine like terms: -20.223748416 + -3 = -23.223748416 x = -23.223748416 Simplifying x = -23.223748416Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.223748416, -23.223748416}
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