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Simplifying 5x2 + 52x + 110 = 0 Reorder the terms: 110 + 52x + 5x2 = 0 Solving 110 + 52x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 22 + 10.4x + x2 = 0 Move the constant term to the right: Add '-22' to each side of the equation. 22 + 10.4x + -22 + x2 = 0 + -22 Reorder the terms: 22 + -22 + 10.4x + x2 = 0 + -22 Combine like terms: 22 + -22 = 0 0 + 10.4x + x2 = 0 + -22 10.4x + x2 = 0 + -22 Combine like terms: 0 + -22 = -22 10.4x + x2 = -22 The x term is 10.4x. Take half its coefficient (5.2). Square it (27.04) and add it to both sides. Add '27.04' to each side of the equation. 10.4x + 27.04 + x2 = -22 + 27.04 Reorder the terms: 27.04 + 10.4x + x2 = -22 + 27.04 Combine like terms: -22 + 27.04 = 5.04 27.04 + 10.4x + x2 = 5.04 Factor a perfect square on the left side: (x + 5.2)(x + 5.2) = 5.04 Calculate the square root of the right side: 2.244994432 Break this problem into two subproblems by setting (x + 5.2) equal to 2.244994432 and -2.244994432.Subproblem 1
x + 5.2 = 2.244994432 Simplifying x + 5.2 = 2.244994432 Reorder the terms: 5.2 + x = 2.244994432 Solving 5.2 + x = 2.244994432 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.2' to each side of the equation. 5.2 + -5.2 + x = 2.244994432 + -5.2 Combine like terms: 5.2 + -5.2 = 0.0 0.0 + x = 2.244994432 + -5.2 x = 2.244994432 + -5.2 Combine like terms: 2.244994432 + -5.2 = -2.955005568 x = -2.955005568 Simplifying x = -2.955005568Subproblem 2
x + 5.2 = -2.244994432 Simplifying x + 5.2 = -2.244994432 Reorder the terms: 5.2 + x = -2.244994432 Solving 5.2 + x = -2.244994432 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.2' to each side of the equation. 5.2 + -5.2 + x = -2.244994432 + -5.2 Combine like terms: 5.2 + -5.2 = 0.0 0.0 + x = -2.244994432 + -5.2 x = -2.244994432 + -5.2 Combine like terms: -2.244994432 + -5.2 = -7.444994432 x = -7.444994432 Simplifying x = -7.444994432Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.955005568, -7.444994432}
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