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Simplifying 2x2 + 42x + 115 = 0 Reorder the terms: 115 + 42x + 2x2 = 0 Solving 115 + 42x + 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'. 57.5 + 21x + x2 = 0 Move the constant term to the right: Add '-57.5' to each side of the equation. 57.5 + 21x + -57.5 + x2 = 0 + -57.5 Reorder the terms: 57.5 + -57.5 + 21x + x2 = 0 + -57.5 Combine like terms: 57.5 + -57.5 = 0.0 0.0 + 21x + x2 = 0 + -57.5 21x + x2 = 0 + -57.5 Combine like terms: 0 + -57.5 = -57.5 21x + x2 = -57.5 The x term is 21x. Take half its coefficient (10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. 21x + 110.25 + x2 = -57.5 + 110.25 Reorder the terms: 110.25 + 21x + x2 = -57.5 + 110.25 Combine like terms: -57.5 + 110.25 = 52.75 110.25 + 21x + x2 = 52.75 Factor a perfect square on the left side: (x + 10.5)(x + 10.5) = 52.75 Calculate the square root of the right side: 7.262919523 Break this problem into two subproblems by setting (x + 10.5) equal to 7.262919523 and -7.262919523.Subproblem 1
x + 10.5 = 7.262919523 Simplifying x + 10.5 = 7.262919523 Reorder the terms: 10.5 + x = 7.262919523 Solving 10.5 + x = 7.262919523 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.5' to each side of the equation. 10.5 + -10.5 + x = 7.262919523 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = 7.262919523 + -10.5 x = 7.262919523 + -10.5 Combine like terms: 7.262919523 + -10.5 = -3.237080477 x = -3.237080477 Simplifying x = -3.237080477Subproblem 2
x + 10.5 = -7.262919523 Simplifying x + 10.5 = -7.262919523 Reorder the terms: 10.5 + x = -7.262919523 Solving 10.5 + x = -7.262919523 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.5' to each side of the equation. 10.5 + -10.5 + x = -7.262919523 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = -7.262919523 + -10.5 x = -7.262919523 + -10.5 Combine like terms: -7.262919523 + -10.5 = -17.762919523 x = -17.762919523 Simplifying x = -17.762919523Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.237080477, -17.762919523}
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