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Simplifying 2x2 + -16x + -23 = -2 Reorder the terms: -23 + -16x + 2x2 = -2 Solving -23 + -16x + 2x2 = -2 Solving for variable 'x'. Reorder the terms: -23 + 2 + -16x + 2x2 = -2 + 2 Combine like terms: -23 + 2 = -21 -21 + -16x + 2x2 = -2 + 2 Combine like terms: -2 + 2 = 0 -21 + -16x + 2x2 = 0 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 = 9.14781507 x = 9.14781507 Simplifying x = 9.14781507Subproblem 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 = -1.14781507 x = -1.14781507 Simplifying x = -1.14781507Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.14781507, -1.14781507}
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