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Simplifying 25X2 + 32X + 3 = 0 Reorder the terms: 3 + 32X + 25X2 = 0 Solving 3 + 32X + 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 + 1.28X + X2 = 0 Move the constant term to the right: Add '-0.12' to each side of the equation. 0.12 + 1.28X + -0.12 + X2 = 0 + -0.12 Reorder the terms: 0.12 + -0.12 + 1.28X + X2 = 0 + -0.12 Combine like terms: 0.12 + -0.12 = 0.00 0.00 + 1.28X + X2 = 0 + -0.12 1.28X + X2 = 0 + -0.12 Combine like terms: 0 + -0.12 = -0.12 1.28X + X2 = -0.12 The X term is 1.28X. Take half its coefficient (0.64). Square it (0.4096) and add it to both sides. Add '0.4096' to each side of the equation. 1.28X + 0.4096 + X2 = -0.12 + 0.4096 Reorder the terms: 0.4096 + 1.28X + X2 = -0.12 + 0.4096 Combine like terms: -0.12 + 0.4096 = 0.2896 0.4096 + 1.28X + X2 = 0.2896 Factor a perfect square on the left side: (X + 0.64)(X + 0.64) = 0.2896 Calculate the square root of the right side: 0.538144962 Break this problem into two subproblems by setting (X + 0.64) equal to 0.538144962 and -0.538144962.Subproblem 1
X + 0.64 = 0.538144962 Simplifying X + 0.64 = 0.538144962 Reorder the terms: 0.64 + X = 0.538144962 Solving 0.64 + X = 0.538144962 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.64' to each side of the equation. 0.64 + -0.64 + X = 0.538144962 + -0.64 Combine like terms: 0.64 + -0.64 = 0.00 0.00 + X = 0.538144962 + -0.64 X = 0.538144962 + -0.64 Combine like terms: 0.538144962 + -0.64 = -0.101855038 X = -0.101855038 Simplifying X = -0.101855038Subproblem 2
X + 0.64 = -0.538144962 Simplifying X + 0.64 = -0.538144962 Reorder the terms: 0.64 + X = -0.538144962 Solving 0.64 + X = -0.538144962 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.64' to each side of the equation. 0.64 + -0.64 + X = -0.538144962 + -0.64 Combine like terms: 0.64 + -0.64 = 0.00 0.00 + X = -0.538144962 + -0.64 X = -0.538144962 + -0.64 Combine like terms: -0.538144962 + -0.64 = -1.178144962 X = -1.178144962 Simplifying X = -1.178144962Solution
The solution to the problem is based on the solutions from the subproblems. X = {-0.101855038, -1.178144962}
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