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Simplifying 0.36x + x2 = 0.82 Solving 0.36x + x2 = 0.82 Solving for variable 'x'. Reorder the terms: -0.82 + 0.36x + x2 = 0.82 + -0.82 Combine like terms: 0.82 + -0.82 = 0.00 -0.82 + 0.36x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '0.82' to each side of the equation. -0.82 + 0.36x + 0.82 + x2 = 0.00 + 0.82 Reorder the terms: -0.82 + 0.82 + 0.36x + x2 = 0.00 + 0.82 Combine like terms: -0.82 + 0.82 = 0.00 0.00 + 0.36x + x2 = 0.00 + 0.82 0.36x + x2 = 0.00 + 0.82 Combine like terms: 0.00 + 0.82 = 0.82 0.36x + x2 = 0.82 The x term is 0.36x. Take half its coefficient (0.18). Square it (0.0324) and add it to both sides. Add '0.0324' to each side of the equation. 0.36x + 0.0324 + x2 = 0.82 + 0.0324 Reorder the terms: 0.0324 + 0.36x + x2 = 0.82 + 0.0324 Combine like terms: 0.82 + 0.0324 = 0.8524 0.0324 + 0.36x + x2 = 0.8524 Factor a perfect square on the left side: (x + 0.18)(x + 0.18) = 0.8524 Calculate the square root of the right side: 0.923255111 Break this problem into two subproblems by setting (x + 0.18) equal to 0.923255111 and -0.923255111.Subproblem 1
x + 0.18 = 0.923255111 Simplifying x + 0.18 = 0.923255111 Reorder the terms: 0.18 + x = 0.923255111 Solving 0.18 + x = 0.923255111 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.18' to each side of the equation. 0.18 + -0.18 + x = 0.923255111 + -0.18 Combine like terms: 0.18 + -0.18 = 0.00 0.00 + x = 0.923255111 + -0.18 x = 0.923255111 + -0.18 Combine like terms: 0.923255111 + -0.18 = 0.743255111 x = 0.743255111 Simplifying x = 0.743255111Subproblem 2
x + 0.18 = -0.923255111 Simplifying x + 0.18 = -0.923255111 Reorder the terms: 0.18 + x = -0.923255111 Solving 0.18 + x = -0.923255111 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.18' to each side of the equation. 0.18 + -0.18 + x = -0.923255111 + -0.18 Combine like terms: 0.18 + -0.18 = 0.00 0.00 + x = -0.923255111 + -0.18 x = -0.923255111 + -0.18 Combine like terms: -0.923255111 + -0.18 = -1.103255111 x = -1.103255111 Simplifying x = -1.103255111Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.743255111, -1.103255111}
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