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Simplifying 12.4x2 + -500x + 5000 = 0 Reorder the terms: 5000 + -500x + 12.4x2 = 0 Solving 5000 + -500x + 12.4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 12.4 the coefficient of the squared term: Divide each side by '12.4'. 403.2258065 + -40.32258065x + x2 = 0 Move the constant term to the right: Add '-403.2258065' to each side of the equation. 403.2258065 + -40.32258065x + -403.2258065 + x2 = 0 + -403.2258065 Reorder the terms: 403.2258065 + -403.2258065 + -40.32258065x + x2 = 0 + -403.2258065 Combine like terms: 403.2258065 + -403.2258065 = 0.0000000 0.0000000 + -40.32258065x + x2 = 0 + -403.2258065 -40.32258065x + x2 = 0 + -403.2258065 Combine like terms: 0 + -403.2258065 = -403.2258065 -40.32258065x + x2 = -403.2258065 The x term is -40.32258065x. Take half its coefficient (-20.16129033). Square it (406.4776278) and add it to both sides. Add '406.4776278' to each side of the equation. -40.32258065x + 406.4776278 + x2 = -403.2258065 + 406.4776278 Reorder the terms: 406.4776278 + -40.32258065x + x2 = -403.2258065 + 406.4776278 Combine like terms: -403.2258065 + 406.4776278 = 3.2518213 406.4776278 + -40.32258065x + x2 = 3.2518213 Factor a perfect square on the left side: (x + -20.16129033)(x + -20.16129033) = 3.2518213 Calculate the square root of the right side: 1.803280705 Break this problem into two subproblems by setting (x + -20.16129033) equal to 1.803280705 and -1.803280705.Subproblem 1
x + -20.16129033 = 1.803280705 Simplifying x + -20.16129033 = 1.803280705 Reorder the terms: -20.16129033 + x = 1.803280705 Solving -20.16129033 + x = 1.803280705 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20.16129033' to each side of the equation. -20.16129033 + 20.16129033 + x = 1.803280705 + 20.16129033 Combine like terms: -20.16129033 + 20.16129033 = 0.00000000 0.00000000 + x = 1.803280705 + 20.16129033 x = 1.803280705 + 20.16129033 Combine like terms: 1.803280705 + 20.16129033 = 21.964571035 x = 21.964571035 Simplifying x = 21.964571035Subproblem 2
x + -20.16129033 = -1.803280705 Simplifying x + -20.16129033 = -1.803280705 Reorder the terms: -20.16129033 + x = -1.803280705 Solving -20.16129033 + x = -1.803280705 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20.16129033' to each side of the equation. -20.16129033 + 20.16129033 + x = -1.803280705 + 20.16129033 Combine like terms: -20.16129033 + 20.16129033 = 0.00000000 0.00000000 + x = -1.803280705 + 20.16129033 x = -1.803280705 + 20.16129033 Combine like terms: -1.803280705 + 20.16129033 = 18.358009625 x = 18.358009625 Simplifying x = 18.358009625Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.964571035, 18.358009625}
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