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Simplifying 8x2 + 9 = 128 + 2x Reorder the terms: 9 + 8x2 = 128 + 2x Solving 9 + 8x2 = 128 + 2x Solving for variable 'x'. Reorder the terms: 9 + -128 + -2x + 8x2 = 128 + 2x + -128 + -2x Combine like terms: 9 + -128 = -119 -119 + -2x + 8x2 = 128 + 2x + -128 + -2x Reorder the terms: -119 + -2x + 8x2 = 128 + -128 + 2x + -2x Combine like terms: 128 + -128 = 0 -119 + -2x + 8x2 = 0 + 2x + -2x -119 + -2x + 8x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -119 + -2x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -14.875 + -0.25x + x2 = 0 Move the constant term to the right: Add '14.875' to each side of the equation. -14.875 + -0.25x + 14.875 + x2 = 0 + 14.875 Reorder the terms: -14.875 + 14.875 + -0.25x + x2 = 0 + 14.875 Combine like terms: -14.875 + 14.875 = 0.000 0.000 + -0.25x + x2 = 0 + 14.875 -0.25x + x2 = 0 + 14.875 Combine like terms: 0 + 14.875 = 14.875 -0.25x + x2 = 14.875 The x term is -0.25x. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25x + 0.015625 + x2 = 14.875 + 0.015625 Reorder the terms: 0.015625 + -0.25x + x2 = 14.875 + 0.015625 Combine like terms: 14.875 + 0.015625 = 14.890625 0.015625 + -0.25x + x2 = 14.890625 Factor a perfect square on the left side: (x + -0.125)(x + -0.125) = 14.890625 Calculate the square root of the right side: 3.85883726 Break this problem into two subproblems by setting (x + -0.125) equal to 3.85883726 and -3.85883726.Subproblem 1
x + -0.125 = 3.85883726 Simplifying x + -0.125 = 3.85883726 Reorder the terms: -0.125 + x = 3.85883726 Solving -0.125 + x = 3.85883726 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = 3.85883726 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = 3.85883726 + 0.125 x = 3.85883726 + 0.125 Combine like terms: 3.85883726 + 0.125 = 3.98383726 x = 3.98383726 Simplifying x = 3.98383726Subproblem 2
x + -0.125 = -3.85883726 Simplifying x + -0.125 = -3.85883726 Reorder the terms: -0.125 + x = -3.85883726 Solving -0.125 + x = -3.85883726 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = -3.85883726 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = -3.85883726 + 0.125 x = -3.85883726 + 0.125 Combine like terms: -3.85883726 + 0.125 = -3.73383726 x = -3.73383726 Simplifying x = -3.73383726Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.98383726, -3.73383726}
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