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Simplifying 8x2 + 21x + -28 = 0 Reorder the terms: -28 + 21x + 8x2 = 0 Solving -28 + 21x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -3.5 + 2.625x + x2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + 2.625x + 3.5 + x2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + 2.625x + x2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + 2.625x + x2 = 0 + 3.5 2.625x + x2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 2.625x + x2 = 3.5 The x term is 2.625x. Take half its coefficient (1.3125). Square it (1.72265625) and add it to both sides. Add '1.72265625' to each side of the equation. 2.625x + 1.72265625 + x2 = 3.5 + 1.72265625 Reorder the terms: 1.72265625 + 2.625x + x2 = 3.5 + 1.72265625 Combine like terms: 3.5 + 1.72265625 = 5.22265625 1.72265625 + 2.625x + x2 = 5.22265625 Factor a perfect square on the left side: (x + 1.3125)(x + 1.3125) = 5.22265625 Calculate the square root of the right side: 2.285313162 Break this problem into two subproblems by setting (x + 1.3125) equal to 2.285313162 and -2.285313162.Subproblem 1
x + 1.3125 = 2.285313162 Simplifying x + 1.3125 = 2.285313162 Reorder the terms: 1.3125 + x = 2.285313162 Solving 1.3125 + x = 2.285313162 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.3125' to each side of the equation. 1.3125 + -1.3125 + x = 2.285313162 + -1.3125 Combine like terms: 1.3125 + -1.3125 = 0.0000 0.0000 + x = 2.285313162 + -1.3125 x = 2.285313162 + -1.3125 Combine like terms: 2.285313162 + -1.3125 = 0.972813162 x = 0.972813162 Simplifying x = 0.972813162Subproblem 2
x + 1.3125 = -2.285313162 Simplifying x + 1.3125 = -2.285313162 Reorder the terms: 1.3125 + x = -2.285313162 Solving 1.3125 + x = -2.285313162 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.3125' to each side of the equation. 1.3125 + -1.3125 + x = -2.285313162 + -1.3125 Combine like terms: 1.3125 + -1.3125 = 0.0000 0.0000 + x = -2.285313162 + -1.3125 x = -2.285313162 + -1.3125 Combine like terms: -2.285313162 + -1.3125 = -3.597813162 x = -3.597813162 Simplifying x = -3.597813162Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.972813162, -3.597813162}
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