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Simplifying 2x2 + 52x + 25 = 0 Reorder the terms: 25 + 52x + 2x2 = 0 Solving 25 + 52x + 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 + 26x + x2 = 0 Move the constant term to the right: Add '-12.5' to each side of the equation. 12.5 + 26x + -12.5 + x2 = 0 + -12.5 Reorder the terms: 12.5 + -12.5 + 26x + x2 = 0 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + 26x + x2 = 0 + -12.5 26x + x2 = 0 + -12.5 Combine like terms: 0 + -12.5 = -12.5 26x + x2 = -12.5 The x term is 26x. Take half its coefficient (13). Square it (169) and add it to both sides. Add '169' to each side of the equation. 26x + 169 + x2 = -12.5 + 169 Reorder the terms: 169 + 26x + x2 = -12.5 + 169 Combine like terms: -12.5 + 169 = 156.5 169 + 26x + x2 = 156.5 Factor a perfect square on the left side: (x + 13)(x + 13) = 156.5 Calculate the square root of the right side: 12.509996003 Break this problem into two subproblems by setting (x + 13) equal to 12.509996003 and -12.509996003.Subproblem 1
x + 13 = 12.509996003 Simplifying x + 13 = 12.509996003 Reorder the terms: 13 + x = 12.509996003 Solving 13 + x = 12.509996003 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + x = 12.509996003 + -13 Combine like terms: 13 + -13 = 0 0 + x = 12.509996003 + -13 x = 12.509996003 + -13 Combine like terms: 12.509996003 + -13 = -0.490003997 x = -0.490003997 Simplifying x = -0.490003997Subproblem 2
x + 13 = -12.509996003 Simplifying x + 13 = -12.509996003 Reorder the terms: 13 + x = -12.509996003 Solving 13 + x = -12.509996003 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + x = -12.509996003 + -13 Combine like terms: 13 + -13 = 0 0 + x = -12.509996003 + -13 x = -12.509996003 + -13 Combine like terms: -12.509996003 + -13 = -25.509996003 x = -25.509996003 Simplifying x = -25.509996003Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.490003997, -25.509996003}
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