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Simplifying 0.05x2 + 2.5x + -323 = 0 Reorder the terms: -323 + 2.5x + 0.05x2 = 0 Solving -323 + 2.5x + 0.05x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.05 the coefficient of the squared term: Divide each side by '0.05'. -6460 + 50x + x2 = 0 Move the constant term to the right: Add '6460' to each side of the equation. -6460 + 50x + 6460 + x2 = 0 + 6460 Reorder the terms: -6460 + 6460 + 50x + x2 = 0 + 6460 Combine like terms: -6460 + 6460 = 0 0 + 50x + x2 = 0 + 6460 50x + x2 = 0 + 6460 Combine like terms: 0 + 6460 = 6460 50x + x2 = 6460 The x term is 50x. Take half its coefficient (25). Square it (625) and add it to both sides. Add '625' to each side of the equation. 50x + 625 + x2 = 6460 + 625 Reorder the terms: 625 + 50x + x2 = 6460 + 625 Combine like terms: 6460 + 625 = 7085 625 + 50x + x2 = 7085 Factor a perfect square on the left side: (x + 25)(x + 25) = 7085 Calculate the square root of the right side: 84.172442046 Break this problem into two subproblems by setting (x + 25) equal to 84.172442046 and -84.172442046.Subproblem 1
x + 25 = 84.172442046 Simplifying x + 25 = 84.172442046 Reorder the terms: 25 + x = 84.172442046 Solving 25 + x = 84.172442046 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + x = 84.172442046 + -25 Combine like terms: 25 + -25 = 0 0 + x = 84.172442046 + -25 x = 84.172442046 + -25 Combine like terms: 84.172442046 + -25 = 59.172442046 x = 59.172442046 Simplifying x = 59.172442046Subproblem 2
x + 25 = -84.172442046 Simplifying x + 25 = -84.172442046 Reorder the terms: 25 + x = -84.172442046 Solving 25 + x = -84.172442046 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + x = -84.172442046 + -25 Combine like terms: 25 + -25 = 0 0 + x = -84.172442046 + -25 x = -84.172442046 + -25 Combine like terms: -84.172442046 + -25 = -109.172442046 x = -109.172442046 Simplifying x = -109.172442046Solution
The solution to the problem is based on the solutions from the subproblems. x = {59.172442046, -109.172442046}
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