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Simplifying 900 + 187x + -1x2 = 0 Solving 900 + 187x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -900 + -187x + x2 = 0 Move the constant term to the right: Add '900' to each side of the equation. -900 + -187x + 900 + x2 = 0 + 900 Reorder the terms: -900 + 900 + -187x + x2 = 0 + 900 Combine like terms: -900 + 900 = 0 0 + -187x + x2 = 0 + 900 -187x + x2 = 0 + 900 Combine like terms: 0 + 900 = 900 -187x + x2 = 900 The x term is -187x. Take half its coefficient (-93.5). Square it (8742.25) and add it to both sides. Add '8742.25' to each side of the equation. -187x + 8742.25 + x2 = 900 + 8742.25 Reorder the terms: 8742.25 + -187x + x2 = 900 + 8742.25 Combine like terms: 900 + 8742.25 = 9642.25 8742.25 + -187x + x2 = 9642.25 Factor a perfect square on the left side: (x + -93.5)(x + -93.5) = 9642.25 Calculate the square root of the right side: 98.194959137 Break this problem into two subproblems by setting (x + -93.5) equal to 98.194959137 and -98.194959137.Subproblem 1
x + -93.5 = 98.194959137 Simplifying x + -93.5 = 98.194959137 Reorder the terms: -93.5 + x = 98.194959137 Solving -93.5 + x = 98.194959137 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '93.5' to each side of the equation. -93.5 + 93.5 + x = 98.194959137 + 93.5 Combine like terms: -93.5 + 93.5 = 0.0 0.0 + x = 98.194959137 + 93.5 x = 98.194959137 + 93.5 Combine like terms: 98.194959137 + 93.5 = 191.694959137 x = 191.694959137 Simplifying x = 191.694959137Subproblem 2
x + -93.5 = -98.194959137 Simplifying x + -93.5 = -98.194959137 Reorder the terms: -93.5 + x = -98.194959137 Solving -93.5 + x = -98.194959137 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '93.5' to each side of the equation. -93.5 + 93.5 + x = -98.194959137 + 93.5 Combine like terms: -93.5 + 93.5 = 0.0 0.0 + x = -98.194959137 + 93.5 x = -98.194959137 + 93.5 Combine like terms: -98.194959137 + 93.5 = -4.694959137 x = -4.694959137 Simplifying x = -4.694959137Solution
The solution to the problem is based on the solutions from the subproblems. x = {191.694959137, -4.694959137}
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