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Simplifying x2 + -105x + -1550 = 0 Reorder the terms: -1550 + -105x + x2 = 0 Solving -1550 + -105x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1550' to each side of the equation. -1550 + -105x + 1550 + x2 = 0 + 1550 Reorder the terms: -1550 + 1550 + -105x + x2 = 0 + 1550 Combine like terms: -1550 + 1550 = 0 0 + -105x + x2 = 0 + 1550 -105x + x2 = 0 + 1550 Combine like terms: 0 + 1550 = 1550 -105x + x2 = 1550 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 = 1550 + 2756.25 Reorder the terms: 2756.25 + -105x + x2 = 1550 + 2756.25 Combine like terms: 1550 + 2756.25 = 4306.25 2756.25 + -105x + x2 = 4306.25 Factor a perfect square on the left side: (x + -52.5)(x + -52.5) = 4306.25 Calculate the square root of the right side: 65.622023742 Break this problem into two subproblems by setting (x + -52.5) equal to 65.622023742 and -65.622023742.Subproblem 1
x + -52.5 = 65.622023742 Simplifying x + -52.5 = 65.622023742 Reorder the terms: -52.5 + x = 65.622023742 Solving -52.5 + x = 65.622023742 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 = 65.622023742 + 52.5 Combine like terms: -52.5 + 52.5 = 0.0 0.0 + x = 65.622023742 + 52.5 x = 65.622023742 + 52.5 Combine like terms: 65.622023742 + 52.5 = 118.122023742 x = 118.122023742 Simplifying x = 118.122023742Subproblem 2
x + -52.5 = -65.622023742 Simplifying x + -52.5 = -65.622023742 Reorder the terms: -52.5 + x = -65.622023742 Solving -52.5 + x = -65.622023742 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 = -65.622023742 + 52.5 Combine like terms: -52.5 + 52.5 = 0.0 0.0 + x = -65.622023742 + 52.5 x = -65.622023742 + 52.5 Combine like terms: -65.622023742 + 52.5 = -13.122023742 x = -13.122023742 Simplifying x = -13.122023742Solution
The solution to the problem is based on the solutions from the subproblems. x = {118.122023742, -13.122023742}
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