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Simplifying 2x2 + 15x + -6.5 = 0 Reorder the terms: -6.5 + 15x + 2x2 = 0 Solving -6.5 + 15x + 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'. -3.25 + 7.5x + x2 = 0 Move the constant term to the right: Add '3.25' to each side of the equation. -3.25 + 7.5x + 3.25 + x2 = 0 + 3.25 Reorder the terms: -3.25 + 3.25 + 7.5x + x2 = 0 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + 7.5x + x2 = 0 + 3.25 7.5x + x2 = 0 + 3.25 Combine like terms: 0 + 3.25 = 3.25 7.5x + x2 = 3.25 The x term is 7.5x. Take half its coefficient (3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. 7.5x + 14.0625 + x2 = 3.25 + 14.0625 Reorder the terms: 14.0625 + 7.5x + x2 = 3.25 + 14.0625 Combine like terms: 3.25 + 14.0625 = 17.3125 14.0625 + 7.5x + x2 = 17.3125 Factor a perfect square on the left side: (x + 3.75)(x + 3.75) = 17.3125 Calculate the square root of the right side: 4.160829244 Break this problem into two subproblems by setting (x + 3.75) equal to 4.160829244 and -4.160829244.Subproblem 1
x + 3.75 = 4.160829244 Simplifying x + 3.75 = 4.160829244 Reorder the terms: 3.75 + x = 4.160829244 Solving 3.75 + x = 4.160829244 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + x = 4.160829244 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = 4.160829244 + -3.75 x = 4.160829244 + -3.75 Combine like terms: 4.160829244 + -3.75 = 0.410829244 x = 0.410829244 Simplifying x = 0.410829244Subproblem 2
x + 3.75 = -4.160829244 Simplifying x + 3.75 = -4.160829244 Reorder the terms: 3.75 + x = -4.160829244 Solving 3.75 + x = -4.160829244 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + x = -4.160829244 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = -4.160829244 + -3.75 x = -4.160829244 + -3.75 Combine like terms: -4.160829244 + -3.75 = -7.910829244 x = -7.910829244 Simplifying x = -7.910829244Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.410829244, -7.910829244}
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