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Simplifying 4x2 + 26x + 25 = 0 Reorder the terms: 25 + 26x + 4x2 = 0 Solving 25 + 26x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 6.25 + 6.5x + x2 = 0 Move the constant term to the right: Add '-6.25' to each side of the equation. 6.25 + 6.5x + -6.25 + x2 = 0 + -6.25 Reorder the terms: 6.25 + -6.25 + 6.5x + x2 = 0 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + 6.5x + x2 = 0 + -6.25 6.5x + x2 = 0 + -6.25 Combine like terms: 0 + -6.25 = -6.25 6.5x + x2 = -6.25 The x term is 6.5x. Take half its coefficient (3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. 6.5x + 10.5625 + x2 = -6.25 + 10.5625 Reorder the terms: 10.5625 + 6.5x + x2 = -6.25 + 10.5625 Combine like terms: -6.25 + 10.5625 = 4.3125 10.5625 + 6.5x + x2 = 4.3125 Factor a perfect square on the left side: (x + 3.25)(x + 3.25) = 4.3125 Calculate the square root of the right side: 2.076655966 Break this problem into two subproblems by setting (x + 3.25) equal to 2.076655966 and -2.076655966.Subproblem 1
x + 3.25 = 2.076655966 Simplifying x + 3.25 = 2.076655966 Reorder the terms: 3.25 + x = 2.076655966 Solving 3.25 + x = 2.076655966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + x = 2.076655966 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = 2.076655966 + -3.25 x = 2.076655966 + -3.25 Combine like terms: 2.076655966 + -3.25 = -1.173344034 x = -1.173344034 Simplifying x = -1.173344034Subproblem 2
x + 3.25 = -2.076655966 Simplifying x + 3.25 = -2.076655966 Reorder the terms: 3.25 + x = -2.076655966 Solving 3.25 + x = -2.076655966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + x = -2.076655966 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = -2.076655966 + -3.25 x = -2.076655966 + -3.25 Combine like terms: -2.076655966 + -3.25 = -5.326655966 x = -5.326655966 Simplifying x = -5.326655966Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.173344034, -5.326655966}
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