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Simplifying (x2) + -9x + -2556 = 0 x2 + -9x + -2556 = 0 Reorder the terms: -2556 + -9x + x2 = 0 Solving -2556 + -9x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '2556' to each side of the equation. -2556 + -9x + 2556 + x2 = 0 + 2556 Reorder the terms: -2556 + 2556 + -9x + x2 = 0 + 2556 Combine like terms: -2556 + 2556 = 0 0 + -9x + x2 = 0 + 2556 -9x + x2 = 0 + 2556 Combine like terms: 0 + 2556 = 2556 -9x + x2 = 2556 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 = 2556 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 2556 + 20.25 Combine like terms: 2556 + 20.25 = 2576.25 20.25 + -9x + x2 = 2576.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 2576.25 Calculate the square root of the right side: 50.756772947 Break this problem into two subproblems by setting (x + -4.5) equal to 50.756772947 and -50.756772947.Subproblem 1
x + -4.5 = 50.756772947 Simplifying x + -4.5 = 50.756772947 Reorder the terms: -4.5 + x = 50.756772947 Solving -4.5 + x = 50.756772947 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 = 50.756772947 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 50.756772947 + 4.5 x = 50.756772947 + 4.5 Combine like terms: 50.756772947 + 4.5 = 55.256772947 x = 55.256772947 Simplifying x = 55.256772947Subproblem 2
x + -4.5 = -50.756772947 Simplifying x + -4.5 = -50.756772947 Reorder the terms: -4.5 + x = -50.756772947 Solving -4.5 + x = -50.756772947 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 = -50.756772947 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -50.756772947 + 4.5 x = -50.756772947 + 4.5 Combine like terms: -50.756772947 + 4.5 = -46.256772947 x = -46.256772947 Simplifying x = -46.256772947Solution
The solution to the problem is based on the solutions from the subproblems. x = {55.256772947, -46.256772947}
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