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Simplifying 2x2 + 26x + 65 = 0 Reorder the terms: 65 + 26x + 2x2 = 0 Solving 65 + 26x + 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'. 32.5 + 13x + x2 = 0 Move the constant term to the right: Add '-32.5' to each side of the equation. 32.5 + 13x + -32.5 + x2 = 0 + -32.5 Reorder the terms: 32.5 + -32.5 + 13x + x2 = 0 + -32.5 Combine like terms: 32.5 + -32.5 = 0.0 0.0 + 13x + x2 = 0 + -32.5 13x + x2 = 0 + -32.5 Combine like terms: 0 + -32.5 = -32.5 13x + x2 = -32.5 The x term is 13x. Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. 13x + 42.25 + x2 = -32.5 + 42.25 Reorder the terms: 42.25 + 13x + x2 = -32.5 + 42.25 Combine like terms: -32.5 + 42.25 = 9.75 42.25 + 13x + x2 = 9.75 Factor a perfect square on the left side: (x + 6.5)(x + 6.5) = 9.75 Calculate the square root of the right side: 3.122498999 Break this problem into two subproblems by setting (x + 6.5) equal to 3.122498999 and -3.122498999.Subproblem 1
x + 6.5 = 3.122498999 Simplifying x + 6.5 = 3.122498999 Reorder the terms: 6.5 + x = 3.122498999 Solving 6.5 + x = 3.122498999 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = 3.122498999 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 3.122498999 + -6.5 x = 3.122498999 + -6.5 Combine like terms: 3.122498999 + -6.5 = -3.377501001 x = -3.377501001 Simplifying x = -3.377501001Subproblem 2
x + 6.5 = -3.122498999 Simplifying x + 6.5 = -3.122498999 Reorder the terms: 6.5 + x = -3.122498999 Solving 6.5 + x = -3.122498999 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = -3.122498999 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -3.122498999 + -6.5 x = -3.122498999 + -6.5 Combine like terms: -3.122498999 + -6.5 = -9.622498999 x = -9.622498999 Simplifying x = -9.622498999Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.377501001, -9.622498999}
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