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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 = 24.0625 18.0625 + 8.5x + x2 = 24.0625 Factor a perfect square on the left side: (x + 4.25)(x + 4.25) = 24.0625 Calculate the square root of the right side: 4.905354218 Break this problem into two subproblems by setting (x + 4.25) equal to 4.905354218 and -4.905354218.Subproblem 1
x + 4.25 = 4.905354218 Simplifying x + 4.25 = 4.905354218 Reorder the terms: 4.25 + x = 4.905354218 Solving 4.25 + x = 4.905354218 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 = 4.905354218 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = 4.905354218 + -4.25 x = 4.905354218 + -4.25 Combine like terms: 4.905354218 + -4.25 = 0.655354218 x = 0.655354218 Simplifying x = 0.655354218Subproblem 2
x + 4.25 = -4.905354218 Simplifying x + 4.25 = -4.905354218 Reorder the terms: 4.25 + x = -4.905354218 Solving 4.25 + x = -4.905354218 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 = -4.905354218 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = -4.905354218 + -4.25 x = -4.905354218 + -4.25 Combine like terms: -4.905354218 + -4.25 = -9.155354218 x = -9.155354218 Simplifying x = -9.155354218Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.655354218, -9.155354218}
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