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Simplifying x2 + 105x + -1350 = 0 Reorder the terms: -1350 + 105x + x2 = 0 Solving -1350 + 105x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1350' to each side of the equation. -1350 + 105x + 1350 + x2 = 0 + 1350 Reorder the terms: -1350 + 1350 + 105x + x2 = 0 + 1350 Combine like terms: -1350 + 1350 = 0 0 + 105x + x2 = 0 + 1350 105x + x2 = 0 + 1350 Combine like terms: 0 + 1350 = 1350 105x + x2 = 1350 The x term is 105x. Take half its coefficient (52.5). Square it (2756.25) and add it to both sides. Add '2756.25' to each side of the equation. 105x + 2756.25 + x2 = 1350 + 2756.25 Reorder the terms: 2756.25 + 105x + x2 = 1350 + 2756.25 Combine like terms: 1350 + 2756.25 = 4106.25 2756.25 + 105x + x2 = 4106.25 Factor a perfect square on the left side: (x + 52.5)(x + 52.5) = 4106.25 Calculate the square root of the right side: 64.08002809 Break this problem into two subproblems by setting (x + 52.5) equal to 64.08002809 and -64.08002809.Subproblem 1
x + 52.5 = 64.08002809 Simplifying x + 52.5 = 64.08002809 Reorder the terms: 52.5 + x = 64.08002809 Solving 52.5 + x = 64.08002809 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-52.5' to each side of the equation. 52.5 + -52.5 + x = 64.08002809 + -52.5 Combine like terms: 52.5 + -52.5 = 0.0 0.0 + x = 64.08002809 + -52.5 x = 64.08002809 + -52.5 Combine like terms: 64.08002809 + -52.5 = 11.58002809 x = 11.58002809 Simplifying x = 11.58002809Subproblem 2
x + 52.5 = -64.08002809 Simplifying x + 52.5 = -64.08002809 Reorder the terms: 52.5 + x = -64.08002809 Solving 52.5 + x = -64.08002809 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-52.5' to each side of the equation. 52.5 + -52.5 + x = -64.08002809 + -52.5 Combine like terms: 52.5 + -52.5 = 0.0 0.0 + x = -64.08002809 + -52.5 x = -64.08002809 + -52.5 Combine like terms: -64.08002809 + -52.5 = -116.58002809 x = -116.58002809 Simplifying x = -116.58002809Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.58002809, -116.58002809}
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