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Simplifying 2x2 + 13x = -16 Reorder the terms: 13x + 2x2 = -16 Solving 13x + 2x2 = -16 Solving for variable 'x'. Reorder the terms: 16 + 13x + 2x2 = -16 + 16 Combine like terms: -16 + 16 = 0 16 + 13x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 8 + 6.5x + x2 = 0 Move the constant term to the right: Add '-8' to each side of the equation. 8 + 6.5x + -8 + x2 = 0 + -8 Reorder the terms: 8 + -8 + 6.5x + x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 6.5x + x2 = 0 + -8 6.5x + x2 = 0 + -8 Combine like terms: 0 + -8 = -8 6.5x + x2 = -8 The x term is 6.5x. Take half its coefficient (3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. 6.5x + 10.5625 + x2 = -8 + 10.5625 Reorder the terms: 10.5625 + 6.5x + x2 = -8 + 10.5625 Combine like terms: -8 + 10.5625 = 2.5625 10.5625 + 6.5x + x2 = 2.5625 Factor a perfect square on the left side: (x + 3.25)(x + 3.25) = 2.5625 Calculate the square root of the right side: 1.600781059 Break this problem into two subproblems by setting (x + 3.25) equal to 1.600781059 and -1.600781059.Subproblem 1
x + 3.25 = 1.600781059 Simplifying x + 3.25 = 1.600781059 Reorder the terms: 3.25 + x = 1.600781059 Solving 3.25 + x = 1.600781059 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + x = 1.600781059 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = 1.600781059 + -3.25 x = 1.600781059 + -3.25 Combine like terms: 1.600781059 + -3.25 = -1.649218941 x = -1.649218941 Simplifying x = -1.649218941Subproblem 2
x + 3.25 = -1.600781059 Simplifying x + 3.25 = -1.600781059 Reorder the terms: 3.25 + x = -1.600781059 Solving 3.25 + x = -1.600781059 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + x = -1.600781059 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = -1.600781059 + -3.25 x = -1.600781059 + -3.25 Combine like terms: -1.600781059 + -3.25 = -4.850781059 x = -4.850781059 Simplifying x = -4.850781059Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.649218941, -4.850781059}
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