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Simplifying 2x2 + 16x + -21 = 0 Reorder the terms: -21 + 16x + 2x2 = 0 Solving -21 + 16x + 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'. -10.5 + 8x + x2 = 0 Move the constant term to the right: Add '10.5' to each side of the equation. -10.5 + 8x + 10.5 + x2 = 0 + 10.5 Reorder the terms: -10.5 + 10.5 + 8x + x2 = 0 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + 8x + x2 = 0 + 10.5 8x + x2 = 0 + 10.5 Combine like terms: 0 + 10.5 = 10.5 8x + x2 = 10.5 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 10.5 + 16 Reorder the terms: 16 + 8x + x2 = 10.5 + 16 Combine like terms: 10.5 + 16 = 26.5 16 + 8x + x2 = 26.5 Factor a perfect square on the left side: (x + 4)(x + 4) = 26.5 Calculate the square root of the right side: 5.14781507 Break this problem into two subproblems by setting (x + 4) equal to 5.14781507 and -5.14781507.Subproblem 1
x + 4 = 5.14781507 Simplifying x + 4 = 5.14781507 Reorder the terms: 4 + x = 5.14781507 Solving 4 + x = 5.14781507 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 5.14781507 + -4 Combine like terms: 4 + -4 = 0 0 + x = 5.14781507 + -4 x = 5.14781507 + -4 Combine like terms: 5.14781507 + -4 = 1.14781507 x = 1.14781507 Simplifying x = 1.14781507Subproblem 2
x + 4 = -5.14781507 Simplifying x + 4 = -5.14781507 Reorder the terms: 4 + x = -5.14781507 Solving 4 + x = -5.14781507 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -5.14781507 + -4 Combine like terms: 4 + -4 = 0 0 + x = -5.14781507 + -4 x = -5.14781507 + -4 Combine like terms: -5.14781507 + -4 = -9.14781507 x = -9.14781507 Simplifying x = -9.14781507Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.14781507, -9.14781507}
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