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Simplifying 5x2 + -28x + -110 = 0 Reorder the terms: -110 + -28x + 5x2 = 0 Solving -110 + -28x + 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 + -5.6x + x2 = 0 Move the constant term to the right: Add '22' to each side of the equation. -22 + -5.6x + 22 + x2 = 0 + 22 Reorder the terms: -22 + 22 + -5.6x + x2 = 0 + 22 Combine like terms: -22 + 22 = 0 0 + -5.6x + x2 = 0 + 22 -5.6x + x2 = 0 + 22 Combine like terms: 0 + 22 = 22 -5.6x + x2 = 22 The x term is -5.6x. Take half its coefficient (-2.8). Square it (7.84) and add it to both sides. Add '7.84' to each side of the equation. -5.6x + 7.84 + x2 = 22 + 7.84 Reorder the terms: 7.84 + -5.6x + x2 = 22 + 7.84 Combine like terms: 22 + 7.84 = 29.84 7.84 + -5.6x + x2 = 29.84 Factor a perfect square on the left side: (x + -2.8)(x + -2.8) = 29.84 Calculate the square root of the right side: 5.462600113 Break this problem into two subproblems by setting (x + -2.8) equal to 5.462600113 and -5.462600113.Subproblem 1
x + -2.8 = 5.462600113 Simplifying x + -2.8 = 5.462600113 Reorder the terms: -2.8 + x = 5.462600113 Solving -2.8 + x = 5.462600113 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.8' to each side of the equation. -2.8 + 2.8 + x = 5.462600113 + 2.8 Combine like terms: -2.8 + 2.8 = 0.0 0.0 + x = 5.462600113 + 2.8 x = 5.462600113 + 2.8 Combine like terms: 5.462600113 + 2.8 = 8.262600113 x = 8.262600113 Simplifying x = 8.262600113Subproblem 2
x + -2.8 = -5.462600113 Simplifying x + -2.8 = -5.462600113 Reorder the terms: -2.8 + x = -5.462600113 Solving -2.8 + x = -5.462600113 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.8' to each side of the equation. -2.8 + 2.8 + x = -5.462600113 + 2.8 Combine like terms: -2.8 + 2.8 = 0.0 0.0 + x = -5.462600113 + 2.8 x = -5.462600113 + 2.8 Combine like terms: -5.462600113 + 2.8 = -2.662600113 x = -2.662600113 Simplifying x = -2.662600113Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.262600113, -2.662600113}
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