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Simplifying 10x2 + x + 0.1 = 1000 Reorder the terms: 0.1 + x + 10x2 = 1000 Solving 0.1 + x + 10x2 = 1000 Solving for variable 'x'. Reorder the terms: 0.1 + -1000 + x + 10x2 = 1000 + -1000 Combine like terms: 0.1 + -1000 = -999.9 -999.9 + x + 10x2 = 1000 + -1000 Combine like terms: 1000 + -1000 = 0 -999.9 + x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -99.99 + 0.1x + x2 = 0 Move the constant term to the right: Add '99.99' to each side of the equation. -99.99 + 0.1x + 99.99 + x2 = 0 + 99.99 Reorder the terms: -99.99 + 99.99 + 0.1x + x2 = 0 + 99.99 Combine like terms: -99.99 + 99.99 = 0.00 0.00 + 0.1x + x2 = 0 + 99.99 0.1x + x2 = 0 + 99.99 Combine like terms: 0 + 99.99 = 99.99 0.1x + x2 = 99.99 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.1x + 0.25 + x2 = 99.99 + 0.25 Reorder the terms: 0.25 + 0.1x + x2 = 99.99 + 0.25 Combine like terms: 99.99 + 0.25 = 100.24 0.25 + 0.1x + x2 = 100.24 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 100.24 Calculate the square root of the right side: 10.011992809 Break this problem into two subproblems by setting (x + 0.5) equal to 10.011992809 and -10.011992809.Subproblem 1
x + 0.5 = 10.011992809 Simplifying x + 0.5 = 10.011992809 Reorder the terms: 0.5 + x = 10.011992809 Solving 0.5 + x = 10.011992809 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 10.011992809 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 10.011992809 + -0.5 x = 10.011992809 + -0.5 Combine like terms: 10.011992809 + -0.5 = 9.511992809 x = 9.511992809 Simplifying x = 9.511992809Subproblem 2
x + 0.5 = -10.011992809 Simplifying x + 0.5 = -10.011992809 Reorder the terms: 0.5 + x = -10.011992809 Solving 0.5 + x = -10.011992809 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -10.011992809 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -10.011992809 + -0.5 x = -10.011992809 + -0.5 Combine like terms: -10.011992809 + -0.5 = -10.511992809 x = -10.511992809 Simplifying x = -10.511992809Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.511992809, -10.511992809}
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