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Simplifying 36x2 + x + -25 = 0 Reorder the terms: -25 + x + 36x2 = 0 Solving -25 + x + 36x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. -0.6944444444 + 0.02777777778x + x2 = 0 Move the constant term to the right: Add '0.6944444444' to each side of the equation. -0.6944444444 + 0.02777777778x + 0.6944444444 + x2 = 0 + 0.6944444444 Reorder the terms: -0.6944444444 + 0.6944444444 + 0.02777777778x + x2 = 0 + 0.6944444444 Combine like terms: -0.6944444444 + 0.6944444444 = 0.0000000000 0.0000000000 + 0.02777777778x + x2 = 0 + 0.6944444444 0.02777777778x + x2 = 0 + 0.6944444444 Combine like terms: 0 + 0.6944444444 = 0.6944444444 0.02777777778x + x2 = 0.6944444444 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. 0.02777777778x + 0.25 + x2 = 0.6944444444 + 0.25 Reorder the terms: 0.25 + 0.02777777778x + x2 = 0.6944444444 + 0.25 Combine like terms: 0.6944444444 + 0.25 = 0.9444444444 0.25 + 0.02777777778x + x2 = 0.9444444444 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.9444444444 Calculate the square root of the right side: 0.971825316 Break this problem into two subproblems by setting (x + 0.5) equal to 0.971825316 and -0.971825316.Subproblem 1
x + 0.5 = 0.971825316 Simplifying x + 0.5 = 0.971825316 Reorder the terms: 0.5 + x = 0.971825316 Solving 0.5 + x = 0.971825316 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 = 0.971825316 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.971825316 + -0.5 x = 0.971825316 + -0.5 Combine like terms: 0.971825316 + -0.5 = 0.471825316 x = 0.471825316 Simplifying x = 0.471825316Subproblem 2
x + 0.5 = -0.971825316 Simplifying x + 0.5 = -0.971825316 Reorder the terms: 0.5 + x = -0.971825316 Solving 0.5 + x = -0.971825316 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 = -0.971825316 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.971825316 + -0.5 x = -0.971825316 + -0.5 Combine like terms: -0.971825316 + -0.5 = -1.471825316 x = -1.471825316 Simplifying x = -1.471825316Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.471825316, -1.471825316}
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