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Simplifying 2x2 + 8x + -309 = 0 Reorder the terms: -309 + 8x + 2x2 = 0 Solving -309 + 8x + 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'. -154.5 + 4x + x2 = 0 Move the constant term to the right: Add '154.5' to each side of the equation. -154.5 + 4x + 154.5 + x2 = 0 + 154.5 Reorder the terms: -154.5 + 154.5 + 4x + x2 = 0 + 154.5 Combine like terms: -154.5 + 154.5 = 0.0 0.0 + 4x + x2 = 0 + 154.5 4x + x2 = 0 + 154.5 Combine like terms: 0 + 154.5 = 154.5 4x + x2 = 154.5 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 154.5 + 4 Reorder the terms: 4 + 4x + x2 = 154.5 + 4 Combine like terms: 154.5 + 4 = 158.5 4 + 4x + x2 = 158.5 Factor a perfect square on the left side: (x + 2)(x + 2) = 158.5 Calculate the square root of the right side: 12.589678312 Break this problem into two subproblems by setting (x + 2) equal to 12.589678312 and -12.589678312.Subproblem 1
x + 2 = 12.589678312 Simplifying x + 2 = 12.589678312 Reorder the terms: 2 + x = 12.589678312 Solving 2 + x = 12.589678312 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 12.589678312 + -2 Combine like terms: 2 + -2 = 0 0 + x = 12.589678312 + -2 x = 12.589678312 + -2 Combine like terms: 12.589678312 + -2 = 10.589678312 x = 10.589678312 Simplifying x = 10.589678312Subproblem 2
x + 2 = -12.589678312 Simplifying x + 2 = -12.589678312 Reorder the terms: 2 + x = -12.589678312 Solving 2 + x = -12.589678312 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -12.589678312 + -2 Combine like terms: 2 + -2 = 0 0 + x = -12.589678312 + -2 x = -12.589678312 + -2 Combine like terms: -12.589678312 + -2 = -14.589678312 x = -14.589678312 Simplifying x = -14.589678312Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.589678312, -14.589678312}
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