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Simplifying 800 + -45x + 0.10x2 = 0 Solving 800 + -45x + 0.10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.10 the coefficient of the squared term: Divide each side by '0.10'. 8000 + -450x + x2 = 0 Move the constant term to the right: Add '-8000' to each side of the equation. 8000 + -450x + -8000 + x2 = 0 + -8000 Reorder the terms: 8000 + -8000 + -450x + x2 = 0 + -8000 Combine like terms: 8000 + -8000 = 0 0 + -450x + x2 = 0 + -8000 -450x + x2 = 0 + -8000 Combine like terms: 0 + -8000 = -8000 -450x + x2 = -8000 The x term is -450x. Take half its coefficient (-225). Square it (50625) and add it to both sides. Add '50625' to each side of the equation. -450x + 50625 + x2 = -8000 + 50625 Reorder the terms: 50625 + -450x + x2 = -8000 + 50625 Combine like terms: -8000 + 50625 = 42625 50625 + -450x + x2 = 42625 Factor a perfect square on the left side: (x + -225)(x + -225) = 42625 Calculate the square root of the right side: 206.458228221 Break this problem into two subproblems by setting (x + -225) equal to 206.458228221 and -206.458228221.Subproblem 1
x + -225 = 206.458228221 Simplifying x + -225 = 206.458228221 Reorder the terms: -225 + x = 206.458228221 Solving -225 + x = 206.458228221 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '225' to each side of the equation. -225 + 225 + x = 206.458228221 + 225 Combine like terms: -225 + 225 = 0 0 + x = 206.458228221 + 225 x = 206.458228221 + 225 Combine like terms: 206.458228221 + 225 = 431.458228221 x = 431.458228221 Simplifying x = 431.458228221Subproblem 2
x + -225 = -206.458228221 Simplifying x + -225 = -206.458228221 Reorder the terms: -225 + x = -206.458228221 Solving -225 + x = -206.458228221 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '225' to each side of the equation. -225 + 225 + x = -206.458228221 + 225 Combine like terms: -225 + 225 = 0 0 + x = -206.458228221 + 225 x = -206.458228221 + 225 Combine like terms: -206.458228221 + 225 = 18.541771779 x = 18.541771779 Simplifying x = 18.541771779Solution
The solution to the problem is based on the solutions from the subproblems. x = {431.458228221, 18.541771779}
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