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Simplifying 8x2 + 2x = 127 Reorder the terms: 2x + 8x2 = 127 Solving 2x + 8x2 = 127 Solving for variable 'x'. Reorder the terms: -127 + 2x + 8x2 = 127 + -127 Combine like terms: 127 + -127 = 0 -127 + 2x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -15.875 + 0.25x + x2 = 0 Move the constant term to the right: Add '15.875' to each side of the equation. -15.875 + 0.25x + 15.875 + x2 = 0 + 15.875 Reorder the terms: -15.875 + 15.875 + 0.25x + x2 = 0 + 15.875 Combine like terms: -15.875 + 15.875 = 0.000 0.000 + 0.25x + x2 = 0 + 15.875 0.25x + x2 = 0 + 15.875 Combine like terms: 0 + 15.875 = 15.875 0.25x + x2 = 15.875 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 = 15.875 + 0.015625 Reorder the terms: 0.015625 + 0.25x + x2 = 15.875 + 0.015625 Combine like terms: 15.875 + 0.015625 = 15.890625 0.015625 + 0.25x + x2 = 15.890625 Factor a perfect square on the left side: (x + 0.125)(x + 0.125) = 15.890625 Calculate the square root of the right side: 3.98630468 Break this problem into two subproblems by setting (x + 0.125) equal to 3.98630468 and -3.98630468.Subproblem 1
x + 0.125 = 3.98630468 Simplifying x + 0.125 = 3.98630468 Reorder the terms: 0.125 + x = 3.98630468 Solving 0.125 + x = 3.98630468 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 = 3.98630468 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = 3.98630468 + -0.125 x = 3.98630468 + -0.125 Combine like terms: 3.98630468 + -0.125 = 3.86130468 x = 3.86130468 Simplifying x = 3.86130468Subproblem 2
x + 0.125 = -3.98630468 Simplifying x + 0.125 = -3.98630468 Reorder the terms: 0.125 + x = -3.98630468 Solving 0.125 + x = -3.98630468 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 = -3.98630468 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = -3.98630468 + -0.125 x = -3.98630468 + -0.125 Combine like terms: -3.98630468 + -0.125 = -4.11130468 x = -4.11130468 Simplifying x = -4.11130468Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.86130468, -4.11130468}
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