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Simplifying x2 + -9x = 440 Reorder the terms: -9x + x2 = 440 Solving -9x + x2 = 440 Solving for variable 'x'. Reorder the terms: -440 + -9x + x2 = 440 + -440 Combine like terms: 440 + -440 = 0 -440 + -9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '440' to each side of the equation. -440 + -9x + 440 + x2 = 0 + 440 Reorder the terms: -440 + 440 + -9x + x2 = 0 + 440 Combine like terms: -440 + 440 = 0 0 + -9x + x2 = 0 + 440 -9x + x2 = 0 + 440 Combine like terms: 0 + 440 = 440 -9x + x2 = 440 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = 440 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 440 + 20.25 Combine like terms: 440 + 20.25 = 460.25 20.25 + -9x + x2 = 460.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 460.25 Calculate the square root of the right side: 21.453437953 Break this problem into two subproblems by setting (x + -4.5) equal to 21.453437953 and -21.453437953.Subproblem 1
x + -4.5 = 21.453437953 Simplifying x + -4.5 = 21.453437953 Reorder the terms: -4.5 + x = 21.453437953 Solving -4.5 + x = 21.453437953 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 21.453437953 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 21.453437953 + 4.5 x = 21.453437953 + 4.5 Combine like terms: 21.453437953 + 4.5 = 25.953437953 x = 25.953437953 Simplifying x = 25.953437953Subproblem 2
x + -4.5 = -21.453437953 Simplifying x + -4.5 = -21.453437953 Reorder the terms: -4.5 + x = -21.453437953 Solving -4.5 + x = -21.453437953 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -21.453437953 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -21.453437953 + 4.5 x = -21.453437953 + 4.5 Combine like terms: -21.453437953 + 4.5 = -16.953437953 x = -16.953437953 Simplifying x = -16.953437953Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.953437953, -16.953437953}
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