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Simplifying 2x2 + 13x + -32 = 0 Reorder the terms: -32 + 13x + 2x2 = 0 Solving -32 + 13x + 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'. -16 + 6.5x + x2 = 0 Move the constant term to the right: Add '16' to each side of the equation. -16 + 6.5x + 16 + x2 = 0 + 16 Reorder the terms: -16 + 16 + 6.5x + x2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 6.5x + x2 = 0 + 16 6.5x + x2 = 0 + 16 Combine like terms: 0 + 16 = 16 6.5x + x2 = 16 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 = 16 + 10.5625 Reorder the terms: 10.5625 + 6.5x + x2 = 16 + 10.5625 Combine like terms: 16 + 10.5625 = 26.5625 10.5625 + 6.5x + x2 = 26.5625 Factor a perfect square on the left side: (x + 3.25)(x + 3.25) = 26.5625 Calculate the square root of the right side: 5.153882032 Break this problem into two subproblems by setting (x + 3.25) equal to 5.153882032 and -5.153882032.Subproblem 1
x + 3.25 = 5.153882032 Simplifying x + 3.25 = 5.153882032 Reorder the terms: 3.25 + x = 5.153882032 Solving 3.25 + x = 5.153882032 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 = 5.153882032 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = 5.153882032 + -3.25 x = 5.153882032 + -3.25 Combine like terms: 5.153882032 + -3.25 = 1.903882032 x = 1.903882032 Simplifying x = 1.903882032Subproblem 2
x + 3.25 = -5.153882032 Simplifying x + 3.25 = -5.153882032 Reorder the terms: 3.25 + x = -5.153882032 Solving 3.25 + x = -5.153882032 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 = -5.153882032 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = -5.153882032 + -3.25 x = -5.153882032 + -3.25 Combine like terms: -5.153882032 + -3.25 = -8.403882032 x = -8.403882032 Simplifying x = -8.403882032Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.903882032, -8.403882032}
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