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Simplifying 2x2 + 17x + 12 = 0 Reorder the terms: 12 + 17x + 2x2 = 0 Solving 12 + 17x + 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'. 6 + 8.5x + x2 = 0 Move the constant term to the right: Add '-6' to each side of the equation. 6 + 8.5x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + 8.5x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 8.5x + x2 = 0 + -6 8.5x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 8.5x + x2 = -6 The x term is 8.5x. Take half its coefficient (4.25). Square it (18.0625) and add it to both sides. Add '18.0625' to each side of the equation. 8.5x + 18.0625 + x2 = -6 + 18.0625 Reorder the terms: 18.0625 + 8.5x + x2 = -6 + 18.0625 Combine like terms: -6 + 18.0625 = 12.0625 18.0625 + 8.5x + x2 = 12.0625 Factor a perfect square on the left side: (x + 4.25)(x + 4.25) = 12.0625 Calculate the square root of the right side: 3.473110997 Break this problem into two subproblems by setting (x + 4.25) equal to 3.473110997 and -3.473110997.Subproblem 1
x + 4.25 = 3.473110997 Simplifying x + 4.25 = 3.473110997 Reorder the terms: 4.25 + x = 3.473110997 Solving 4.25 + x = 3.473110997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + x = 3.473110997 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = 3.473110997 + -4.25 x = 3.473110997 + -4.25 Combine like terms: 3.473110997 + -4.25 = -0.776889003 x = -0.776889003 Simplifying x = -0.776889003Subproblem 2
x + 4.25 = -3.473110997 Simplifying x + 4.25 = -3.473110997 Reorder the terms: 4.25 + x = -3.473110997 Solving 4.25 + x = -3.473110997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + x = -3.473110997 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = -3.473110997 + -4.25 x = -3.473110997 + -4.25 Combine like terms: -3.473110997 + -4.25 = -7.723110997 x = -7.723110997 Simplifying x = -7.723110997Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.776889003, -7.723110997}
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