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Simplifying x2 + -6x = 440 Reorder the terms: -6x + x2 = 440 Solving -6x + x2 = 440 Solving for variable 'x'. Reorder the terms: -440 + -6x + x2 = 440 + -440 Combine like terms: 440 + -440 = 0 -440 + -6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '440' to each side of the equation. -440 + -6x + 440 + x2 = 0 + 440 Reorder the terms: -440 + 440 + -6x + x2 = 0 + 440 Combine like terms: -440 + 440 = 0 0 + -6x + x2 = 0 + 440 -6x + x2 = 0 + 440 Combine like terms: 0 + 440 = 440 -6x + x2 = 440 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 = 440 + 9 Reorder the terms: 9 + -6x + x2 = 440 + 9 Combine like terms: 440 + 9 = 449 9 + -6x + x2 = 449 Factor a perfect square on the left side: (x + -3)(x + -3) = 449 Calculate the square root of the right side: 21.1896201 Break this problem into two subproblems by setting (x + -3) equal to 21.1896201 and -21.1896201.Subproblem 1
x + -3 = 21.1896201 Simplifying x + -3 = 21.1896201 Reorder the terms: -3 + x = 21.1896201 Solving -3 + x = 21.1896201 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 = 21.1896201 + 3 Combine like terms: -3 + 3 = 0 0 + x = 21.1896201 + 3 x = 21.1896201 + 3 Combine like terms: 21.1896201 + 3 = 24.1896201 x = 24.1896201 Simplifying x = 24.1896201Subproblem 2
x + -3 = -21.1896201 Simplifying x + -3 = -21.1896201 Reorder the terms: -3 + x = -21.1896201 Solving -3 + x = -21.1896201 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 = -21.1896201 + 3 Combine like terms: -3 + 3 = 0 0 + x = -21.1896201 + 3 x = -21.1896201 + 3 Combine like terms: -21.1896201 + 3 = -18.1896201 x = -18.1896201 Simplifying x = -18.1896201Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.1896201, -18.1896201}
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