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Simplifying 2x2 + 14x + -149 = 0 Reorder the terms: -149 + 14x + 2x2 = 0 Solving -149 + 14x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -74.5 + 7x + x2 = 0 Move the constant term to the right: Add '74.5' to each side of the equation. -74.5 + 7x + 74.5 + x2 = 0 + 74.5 Reorder the terms: -74.5 + 74.5 + 7x + x2 = 0 + 74.5 Combine like terms: -74.5 + 74.5 = 0.0 0.0 + 7x + x2 = 0 + 74.5 7x + x2 = 0 + 74.5 Combine like terms: 0 + 74.5 = 74.5 7x + x2 = 74.5 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = 74.5 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 74.5 + 12.25 Combine like terms: 74.5 + 12.25 = 86.75 12.25 + 7x + x2 = 86.75 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 86.75 Calculate the square root of the right side: 9.313968005 Break this problem into two subproblems by setting (x + 3.5) equal to 9.313968005 and -9.313968005.Subproblem 1
x + 3.5 = 9.313968005 Simplifying x + 3.5 = 9.313968005 Reorder the terms: 3.5 + x = 9.313968005 Solving 3.5 + x = 9.313968005 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 9.313968005 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 9.313968005 + -3.5 x = 9.313968005 + -3.5 Combine like terms: 9.313968005 + -3.5 = 5.813968005 x = 5.813968005 Simplifying x = 5.813968005Subproblem 2
x + 3.5 = -9.313968005 Simplifying x + 3.5 = -9.313968005 Reorder the terms: 3.5 + x = -9.313968005 Solving 3.5 + x = -9.313968005 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -9.313968005 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -9.313968005 + -3.5 x = -9.313968005 + -3.5 Combine like terms: -9.313968005 + -3.5 = -12.813968005 x = -12.813968005 Simplifying x = -12.813968005Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.813968005, -12.813968005}
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