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Simplifying x2 + -9x + -8250 = 0 Reorder the terms: -8250 + -9x + x2 = 0 Solving -8250 + -9x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '8250' to each side of the equation. -8250 + -9x + 8250 + x2 = 0 + 8250 Reorder the terms: -8250 + 8250 + -9x + x2 = 0 + 8250 Combine like terms: -8250 + 8250 = 0 0 + -9x + x2 = 0 + 8250 -9x + x2 = 0 + 8250 Combine like terms: 0 + 8250 = 8250 -9x + x2 = 8250 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 = 8250 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 8250 + 20.25 Combine like terms: 8250 + 20.25 = 8270.25 20.25 + -9x + x2 = 8270.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 8270.25 Calculate the square root of the right side: 90.940914884 Break this problem into two subproblems by setting (x + -4.5) equal to 90.940914884 and -90.940914884.Subproblem 1
x + -4.5 = 90.940914884 Simplifying x + -4.5 = 90.940914884 Reorder the terms: -4.5 + x = 90.940914884 Solving -4.5 + x = 90.940914884 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 = 90.940914884 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 90.940914884 + 4.5 x = 90.940914884 + 4.5 Combine like terms: 90.940914884 + 4.5 = 95.440914884 x = 95.440914884 Simplifying x = 95.440914884Subproblem 2
x + -4.5 = -90.940914884 Simplifying x + -4.5 = -90.940914884 Reorder the terms: -4.5 + x = -90.940914884 Solving -4.5 + x = -90.940914884 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 = -90.940914884 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -90.940914884 + 4.5 x = -90.940914884 + 4.5 Combine like terms: -90.940914884 + 4.5 = -86.440914884 x = -86.440914884 Simplifying x = -86.440914884Solution
The solution to the problem is based on the solutions from the subproblems. x = {95.440914884, -86.440914884}
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