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Simplifying 4x2 + 28x + 25 = 0 Reorder the terms: 25 + 28x + 4x2 = 0 Solving 25 + 28x + 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 + 7x + x2 = 0 Move the constant term to the right: Add '-6.25' to each side of the equation. 6.25 + 7x + -6.25 + x2 = 0 + -6.25 Reorder the terms: 6.25 + -6.25 + 7x + x2 = 0 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + 7x + x2 = 0 + -6.25 7x + x2 = 0 + -6.25 Combine like terms: 0 + -6.25 = -6.25 7x + x2 = -6.25 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = -6.25 + 12.25 Reorder the terms: 12.25 + 7x + x2 = -6.25 + 12.25 Combine like terms: -6.25 + 12.25 = 6 12.25 + 7x + x2 = 6 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (x + 3.5) equal to 2.449489743 and -2.449489743.Subproblem 1
x + 3.5 = 2.449489743 Simplifying x + 3.5 = 2.449489743 Reorder the terms: 3.5 + x = 2.449489743 Solving 3.5 + x = 2.449489743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 2.449489743 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 2.449489743 + -3.5 x = 2.449489743 + -3.5 Combine like terms: 2.449489743 + -3.5 = -1.050510257 x = -1.050510257 Simplifying x = -1.050510257Subproblem 2
x + 3.5 = -2.449489743 Simplifying x + 3.5 = -2.449489743 Reorder the terms: 3.5 + x = -2.449489743 Solving 3.5 + x = -2.449489743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -2.449489743 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -2.449489743 + -3.5 x = -2.449489743 + -3.5 Combine like terms: -2.449489743 + -3.5 = -5.949489743 x = -5.949489743 Simplifying x = -5.949489743Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.050510257, -5.949489743}
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