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Simplifying 10x + 44.22x2 = 0.62 Solving 10x + 44.22x2 = 0.62 Solving for variable 'x'. Reorder the terms: -0.62 + 10x + 44.22x2 = 0.62 + -0.62 Combine like terms: 0.62 + -0.62 = 0.00 -0.62 + 10x + 44.22x2 = 0.00 Begin completing the square. Divide all terms by 44.22 the coefficient of the squared term: Divide each side by '44.22'. -0.01402080507 + 0.2261420172x + x2 = 0 Move the constant term to the right: Add '0.01402080507' to each side of the equation. -0.01402080507 + 0.2261420172x + 0.01402080507 + x2 = 0 + 0.01402080507 Reorder the terms: -0.01402080507 + 0.01402080507 + 0.2261420172x + x2 = 0 + 0.01402080507 Combine like terms: -0.01402080507 + 0.01402080507 = 0.00000000000 0.00000000000 + 0.2261420172x + x2 = 0 + 0.01402080507 0.2261420172x + x2 = 0 + 0.01402080507 Combine like terms: 0 + 0.01402080507 = 0.01402080507 0.2261420172x + x2 = 0.01402080507 The x term is 0.2261420172x. Take half its coefficient (0.1130710086). Square it (0.01278505299) and add it to both sides. Add '0.01278505299' to each side of the equation. 0.2261420172x + 0.01278505299 + x2 = 0.01402080507 + 0.01278505299 Reorder the terms: 0.01278505299 + 0.2261420172x + x2 = 0.01402080507 + 0.01278505299 Combine like terms: 0.01402080507 + 0.01278505299 = 0.02680585806 0.01278505299 + 0.2261420172x + x2 = 0.02680585806 Factor a perfect square on the left side: (x + 0.1130710086)(x + 0.1130710086) = 0.02680585806 Calculate the square root of the right side: 0.163724946 Break this problem into two subproblems by setting (x + 0.1130710086) equal to 0.163724946 and -0.163724946.Subproblem 1
x + 0.1130710086 = 0.163724946 Simplifying x + 0.1130710086 = 0.163724946 Reorder the terms: 0.1130710086 + x = 0.163724946 Solving 0.1130710086 + x = 0.163724946 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1130710086' to each side of the equation. 0.1130710086 + -0.1130710086 + x = 0.163724946 + -0.1130710086 Combine like terms: 0.1130710086 + -0.1130710086 = 0.0000000000 0.0000000000 + x = 0.163724946 + -0.1130710086 x = 0.163724946 + -0.1130710086 Combine like terms: 0.163724946 + -0.1130710086 = 0.0506539374 x = 0.0506539374 Simplifying x = 0.0506539374Subproblem 2
x + 0.1130710086 = -0.163724946 Simplifying x + 0.1130710086 = -0.163724946 Reorder the terms: 0.1130710086 + x = -0.163724946 Solving 0.1130710086 + x = -0.163724946 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1130710086' to each side of the equation. 0.1130710086 + -0.1130710086 + x = -0.163724946 + -0.1130710086 Combine like terms: 0.1130710086 + -0.1130710086 = 0.0000000000 0.0000000000 + x = -0.163724946 + -0.1130710086 x = -0.163724946 + -0.1130710086 Combine like terms: -0.163724946 + -0.1130710086 = -0.2767959546 x = -0.2767959546 Simplifying x = -0.2767959546Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.0506539374, -0.2767959546}
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