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Simplifying 25x2 + 36x + 3 = 0 Reorder the terms: 3 + 36x + 25x2 = 0 Solving 3 + 36x + 25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. 0.12 + 1.44x + x2 = 0 Move the constant term to the right: Add '-0.12' to each side of the equation. 0.12 + 1.44x + -0.12 + x2 = 0 + -0.12 Reorder the terms: 0.12 + -0.12 + 1.44x + x2 = 0 + -0.12 Combine like terms: 0.12 + -0.12 = 0.00 0.00 + 1.44x + x2 = 0 + -0.12 1.44x + x2 = 0 + -0.12 Combine like terms: 0 + -0.12 = -0.12 1.44x + x2 = -0.12 The x term is 1.44x. Take half its coefficient (0.72). Square it (0.5184) and add it to both sides. Add '0.5184' to each side of the equation. 1.44x + 0.5184 + x2 = -0.12 + 0.5184 Reorder the terms: 0.5184 + 1.44x + x2 = -0.12 + 0.5184 Combine like terms: -0.12 + 0.5184 = 0.3984 0.5184 + 1.44x + x2 = 0.3984 Factor a perfect square on the left side: (x + 0.72)(x + 0.72) = 0.3984 Calculate the square root of the right side: 0.631189354 Break this problem into two subproblems by setting (x + 0.72) equal to 0.631189354 and -0.631189354.Subproblem 1
x + 0.72 = 0.631189354 Simplifying x + 0.72 = 0.631189354 Reorder the terms: 0.72 + x = 0.631189354 Solving 0.72 + x = 0.631189354 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.72' to each side of the equation. 0.72 + -0.72 + x = 0.631189354 + -0.72 Combine like terms: 0.72 + -0.72 = 0.00 0.00 + x = 0.631189354 + -0.72 x = 0.631189354 + -0.72 Combine like terms: 0.631189354 + -0.72 = -0.088810646 x = -0.088810646 Simplifying x = -0.088810646Subproblem 2
x + 0.72 = -0.631189354 Simplifying x + 0.72 = -0.631189354 Reorder the terms: 0.72 + x = -0.631189354 Solving 0.72 + x = -0.631189354 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.72' to each side of the equation. 0.72 + -0.72 + x = -0.631189354 + -0.72 Combine like terms: 0.72 + -0.72 = 0.00 0.00 + x = -0.631189354 + -0.72 x = -0.631189354 + -0.72 Combine like terms: -0.631189354 + -0.72 = -1.351189354 x = -1.351189354 Simplifying x = -1.351189354Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.088810646, -1.351189354}
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