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Simplifying 400 = x(x + -6) Reorder the terms: 400 = x(-6 + x) 400 = (-6 * x + x * x) 400 = (-6x + x2) Solving 400 = -6x + x2 Solving for variable 'x'. Reorder the terms: 400 + 6x + -1x2 = -6x + 6x + x2 + -1x2 Combine like terms: -6x + 6x = 0 400 + 6x + -1x2 = 0 + x2 + -1x2 400 + 6x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 400 + 6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -400 + -6x + x2 = 0 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 = 23.223748416 x = 23.223748416 Simplifying x = 23.223748416Subproblem 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 = -17.223748416 x = -17.223748416 Simplifying x = -17.223748416Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.223748416, -17.223748416}
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