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Simplifying 4x2 + 120x + 497 = 0 Reorder the terms: 497 + 120x + 4x2 = 0 Solving 497 + 120x + 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'. 124.25 + 30x + x2 = 0 Move the constant term to the right: Add '-124.25' to each side of the equation. 124.25 + 30x + -124.25 + x2 = 0 + -124.25 Reorder the terms: 124.25 + -124.25 + 30x + x2 = 0 + -124.25 Combine like terms: 124.25 + -124.25 = 0.00 0.00 + 30x + x2 = 0 + -124.25 30x + x2 = 0 + -124.25 Combine like terms: 0 + -124.25 = -124.25 30x + x2 = -124.25 The x term is 30x. Take half its coefficient (15). Square it (225) and add it to both sides. Add '225' to each side of the equation. 30x + 225 + x2 = -124.25 + 225 Reorder the terms: 225 + 30x + x2 = -124.25 + 225 Combine like terms: -124.25 + 225 = 100.75 225 + 30x + x2 = 100.75 Factor a perfect square on the left side: (x + 15)(x + 15) = 100.75 Calculate the square root of the right side: 10.03742995 Break this problem into two subproblems by setting (x + 15) equal to 10.03742995 and -10.03742995.Subproblem 1
x + 15 = 10.03742995 Simplifying x + 15 = 10.03742995 Reorder the terms: 15 + x = 10.03742995 Solving 15 + x = 10.03742995 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = 10.03742995 + -15 Combine like terms: 15 + -15 = 0 0 + x = 10.03742995 + -15 x = 10.03742995 + -15 Combine like terms: 10.03742995 + -15 = -4.96257005 x = -4.96257005 Simplifying x = -4.96257005Subproblem 2
x + 15 = -10.03742995 Simplifying x + 15 = -10.03742995 Reorder the terms: 15 + x = -10.03742995 Solving 15 + x = -10.03742995 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = -10.03742995 + -15 Combine like terms: 15 + -15 = 0 0 + x = -10.03742995 + -15 x = -10.03742995 + -15 Combine like terms: -10.03742995 + -15 = -25.03742995 x = -25.03742995 Simplifying x = -25.03742995Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.96257005, -25.03742995}
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