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Simplifying 0.1x2 + 71x + 100 = 0 Reorder the terms: 100 + 71x + 0.1x2 = 0 Solving 100 + 71x + 0.1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.1 the coefficient of the squared term: Divide each side by '0.1'. 1000 + 710x + x2 = 0 Move the constant term to the right: Add '-1000' to each side of the equation. 1000 + 710x + -1000 + x2 = 0 + -1000 Reorder the terms: 1000 + -1000 + 710x + x2 = 0 + -1000 Combine like terms: 1000 + -1000 = 0 0 + 710x + x2 = 0 + -1000 710x + x2 = 0 + -1000 Combine like terms: 0 + -1000 = -1000 710x + x2 = -1000 The x term is 710x. Take half its coefficient (355). Square it (126025) and add it to both sides. Add '126025' to each side of the equation. 710x + 126025 + x2 = -1000 + 126025 Reorder the terms: 126025 + 710x + x2 = -1000 + 126025 Combine like terms: -1000 + 126025 = 125025 126025 + 710x + x2 = 125025 Factor a perfect square on the left side: (x + 355)(x + 355) = 125025 Calculate the square root of the right side: 353.588744165 Break this problem into two subproblems by setting (x + 355) equal to 353.588744165 and -353.588744165.Subproblem 1
x + 355 = 353.588744165 Simplifying x + 355 = 353.588744165 Reorder the terms: 355 + x = 353.588744165 Solving 355 + x = 353.588744165 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-355' to each side of the equation. 355 + -355 + x = 353.588744165 + -355 Combine like terms: 355 + -355 = 0 0 + x = 353.588744165 + -355 x = 353.588744165 + -355 Combine like terms: 353.588744165 + -355 = -1.411255835 x = -1.411255835 Simplifying x = -1.411255835Subproblem 2
x + 355 = -353.588744165 Simplifying x + 355 = -353.588744165 Reorder the terms: 355 + x = -353.588744165 Solving 355 + x = -353.588744165 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-355' to each side of the equation. 355 + -355 + x = -353.588744165 + -355 Combine like terms: 355 + -355 = 0 0 + x = -353.588744165 + -355 x = -353.588744165 + -355 Combine like terms: -353.588744165 + -355 = -708.588744165 x = -708.588744165 Simplifying x = -708.588744165Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.411255835, -708.588744165}
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