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Simplifying 2x2 + 16x + 25 = 0 Reorder the terms: 25 + 16x + 2x2 = 0 Solving 25 + 16x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 12.5 + 8x + x2 = 0 Move the constant term to the right: Add '-12.5' to each side of the equation. 12.5 + 8x + -12.5 + x2 = 0 + -12.5 Reorder the terms: 12.5 + -12.5 + 8x + x2 = 0 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + 8x + x2 = 0 + -12.5 8x + x2 = 0 + -12.5 Combine like terms: 0 + -12.5 = -12.5 8x + x2 = -12.5 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = -12.5 + 16 Reorder the terms: 16 + 8x + x2 = -12.5 + 16 Combine like terms: -12.5 + 16 = 3.5 16 + 8x + x2 = 3.5 Factor a perfect square on the left side: (x + 4)(x + 4) = 3.5 Calculate the square root of the right side: 1.870828693 Break this problem into two subproblems by setting (x + 4) equal to 1.870828693 and -1.870828693.Subproblem 1
x + 4 = 1.870828693 Simplifying x + 4 = 1.870828693 Reorder the terms: 4 + x = 1.870828693 Solving 4 + x = 1.870828693 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 1.870828693 + -4 Combine like terms: 4 + -4 = 0 0 + x = 1.870828693 + -4 x = 1.870828693 + -4 Combine like terms: 1.870828693 + -4 = -2.129171307 x = -2.129171307 Simplifying x = -2.129171307Subproblem 2
x + 4 = -1.870828693 Simplifying x + 4 = -1.870828693 Reorder the terms: 4 + x = -1.870828693 Solving 4 + x = -1.870828693 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -1.870828693 + -4 Combine like terms: 4 + -4 = 0 0 + x = -1.870828693 + -4 x = -1.870828693 + -4 Combine like terms: -1.870828693 + -4 = -5.870828693 x = -5.870828693 Simplifying x = -5.870828693Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.129171307, -5.870828693}
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