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Simplifying 4x2 + 16x + 20x + 80 = 115 Reorder the terms: 80 + 16x + 20x + 4x2 = 115 Combine like terms: 16x + 20x = 36x 80 + 36x + 4x2 = 115 Solving 80 + 36x + 4x2 = 115 Solving for variable 'x'. Reorder the terms: 80 + -115 + 36x + 4x2 = 115 + -115 Combine like terms: 80 + -115 = -35 -35 + 36x + 4x2 = 115 + -115 Combine like terms: 115 + -115 = 0 -35 + 36x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -8.75 + 9x + x2 = 0 Move the constant term to the right: Add '8.75' to each side of the equation. -8.75 + 9x + 8.75 + x2 = 0 + 8.75 Reorder the terms: -8.75 + 8.75 + 9x + x2 = 0 + 8.75 Combine like terms: -8.75 + 8.75 = 0.00 0.00 + 9x + x2 = 0 + 8.75 9x + x2 = 0 + 8.75 Combine like terms: 0 + 8.75 = 8.75 9x + x2 = 8.75 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = 8.75 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 8.75 + 20.25 Combine like terms: 8.75 + 20.25 = 29 20.25 + 9x + x2 = 29 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 29 Calculate the square root of the right side: 5.385164807 Break this problem into two subproblems by setting (x + 4.5) equal to 5.385164807 and -5.385164807.Subproblem 1
x + 4.5 = 5.385164807 Simplifying x + 4.5 = 5.385164807 Reorder the terms: 4.5 + x = 5.385164807 Solving 4.5 + x = 5.385164807 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 5.385164807 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 5.385164807 + -4.5 x = 5.385164807 + -4.5 Combine like terms: 5.385164807 + -4.5 = 0.885164807 x = 0.885164807 Simplifying x = 0.885164807Subproblem 2
x + 4.5 = -5.385164807 Simplifying x + 4.5 = -5.385164807 Reorder the terms: 4.5 + x = -5.385164807 Solving 4.5 + x = -5.385164807 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -5.385164807 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -5.385164807 + -4.5 x = -5.385164807 + -4.5 Combine like terms: -5.385164807 + -4.5 = -9.885164807 x = -9.885164807 Simplifying x = -9.885164807Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.885164807, -9.885164807}
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