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Simplifying 4x2 + 20x + -91 = 0 Reorder the terms: -91 + 20x + 4x2 = 0 Solving -91 + 20x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -22.75 + 5x + x2 = 0 Move the constant term to the right: Add '22.75' to each side of the equation. -22.75 + 5x + 22.75 + x2 = 0 + 22.75 Reorder the terms: -22.75 + 22.75 + 5x + x2 = 0 + 22.75 Combine like terms: -22.75 + 22.75 = 0.00 0.00 + 5x + x2 = 0 + 22.75 5x + x2 = 0 + 22.75 Combine like terms: 0 + 22.75 = 22.75 5x + x2 = 22.75 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 22.75 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 22.75 + 6.25 Combine like terms: 22.75 + 6.25 = 29 6.25 + 5x + x2 = 29 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 29 Calculate the square root of the right side: 5.385164807 Break this problem into two subproblems by setting (x + 2.5) equal to 5.385164807 and -5.385164807.Subproblem 1
x + 2.5 = 5.385164807 Simplifying x + 2.5 = 5.385164807 Reorder the terms: 2.5 + x = 5.385164807 Solving 2.5 + x = 5.385164807 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 5.385164807 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 5.385164807 + -2.5 x = 5.385164807 + -2.5 Combine like terms: 5.385164807 + -2.5 = 2.885164807 x = 2.885164807 Simplifying x = 2.885164807Subproblem 2
x + 2.5 = -5.385164807 Simplifying x + 2.5 = -5.385164807 Reorder the terms: 2.5 + x = -5.385164807 Solving 2.5 + x = -5.385164807 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -5.385164807 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -5.385164807 + -2.5 x = -5.385164807 + -2.5 Combine like terms: -5.385164807 + -2.5 = -7.885164807 x = -7.885164807 Simplifying x = -7.885164807Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.885164807, -7.885164807}
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