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Simplifying 1.24x2 + -500x + -5000 = 0 Reorder the terms: -5000 + -500x + 1.24x2 = 0 Solving -5000 + -500x + 1.24x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 1.24 the coefficient of the squared term: Divide each side by '1.24'. -4032.258065 + -403.2258065x + x2 = 0 Move the constant term to the right: Add '4032.258065' to each side of the equation. -4032.258065 + -403.2258065x + 4032.258065 + x2 = 0 + 4032.258065 Reorder the terms: -4032.258065 + 4032.258065 + -403.2258065x + x2 = 0 + 4032.258065 Combine like terms: -4032.258065 + 4032.258065 = 0.000000 0.000000 + -403.2258065x + x2 = 0 + 4032.258065 -403.2258065x + x2 = 0 + 4032.258065 Combine like terms: 0 + 4032.258065 = 4032.258065 -403.2258065x + x2 = 4032.258065 The x term is -403.2258065x. Take half its coefficient (-201.6129033). Square it (40647.76278) and add it to both sides. Add '40647.76278' to each side of the equation. -403.2258065x + 40647.76278 + x2 = 4032.258065 + 40647.76278 Reorder the terms: 40647.76278 + -403.2258065x + x2 = 4032.258065 + 40647.76278 Combine like terms: 4032.258065 + 40647.76278 = 44680.020845 40647.76278 + -403.2258065x + x2 = 44680.020845 Factor a perfect square on the left side: (x + -201.6129033)(x + -201.6129033) = 44680.020845 Calculate the square root of the right side: 211.376490758 Break this problem into two subproblems by setting (x + -201.6129033) equal to 211.376490758 and -211.376490758.Subproblem 1
x + -201.6129033 = 211.376490758 Simplifying x + -201.6129033 = 211.376490758 Reorder the terms: -201.6129033 + x = 211.376490758 Solving -201.6129033 + x = 211.376490758 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '201.6129033' to each side of the equation. -201.6129033 + 201.6129033 + x = 211.376490758 + 201.6129033 Combine like terms: -201.6129033 + 201.6129033 = 0.0000000 0.0000000 + x = 211.376490758 + 201.6129033 x = 211.376490758 + 201.6129033 Combine like terms: 211.376490758 + 201.6129033 = 412.989394058 x = 412.989394058 Simplifying x = 412.989394058Subproblem 2
x + -201.6129033 = -211.376490758 Simplifying x + -201.6129033 = -211.376490758 Reorder the terms: -201.6129033 + x = -211.376490758 Solving -201.6129033 + x = -211.376490758 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '201.6129033' to each side of the equation. -201.6129033 + 201.6129033 + x = -211.376490758 + 201.6129033 Combine like terms: -201.6129033 + 201.6129033 = 0.0000000 0.0000000 + x = -211.376490758 + 201.6129033 x = -211.376490758 + 201.6129033 Combine like terms: -211.376490758 + 201.6129033 = -9.763587458 x = -9.763587458 Simplifying x = -9.763587458Solution
The solution to the problem is based on the solutions from the subproblems. x = {412.989394058, -9.763587458}
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