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Simplifying 8x2 + 2x = 25 + x Reorder the terms: 2x + 8x2 = 25 + x Solving 2x + 8x2 = 25 + x Solving for variable 'x'. Reorder the terms: -25 + 2x + -1x + 8x2 = 25 + x + -25 + -1x Combine like terms: 2x + -1x = 1x -25 + 1x + 8x2 = 25 + x + -25 + -1x Reorder the terms: -25 + 1x + 8x2 = 25 + -25 + x + -1x Combine like terms: 25 + -25 = 0 -25 + 1x + 8x2 = 0 + x + -1x -25 + 1x + 8x2 = x + -1x Combine like terms: x + -1x = 0 -25 + 1x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -3.125 + 0.125x + x2 = 0 Move the constant term to the right: Add '3.125' to each side of the equation. -3.125 + 0.125x + 3.125 + x2 = 0 + 3.125 Reorder the terms: -3.125 + 3.125 + 0.125x + x2 = 0 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + 0.125x + x2 = 0 + 3.125 0.125x + x2 = 0 + 3.125 Combine like terms: 0 + 3.125 = 3.125 0.125x + x2 = 3.125 The x term is 0.125x. Take half its coefficient (0.0625). Square it (0.00390625) and add it to both sides. Add '0.00390625' to each side of the equation. 0.125x + 0.00390625 + x2 = 3.125 + 0.00390625 Reorder the terms: 0.00390625 + 0.125x + x2 = 3.125 + 0.00390625 Combine like terms: 3.125 + 0.00390625 = 3.12890625 0.00390625 + 0.125x + x2 = 3.12890625 Factor a perfect square on the left side: (x + 0.0625)(x + 0.0625) = 3.12890625 Calculate the square root of the right side: 1.768871462 Break this problem into two subproblems by setting (x + 0.0625) equal to 1.768871462 and -1.768871462.Subproblem 1
x + 0.0625 = 1.768871462 Simplifying x + 0.0625 = 1.768871462 Reorder the terms: 0.0625 + x = 1.768871462 Solving 0.0625 + x = 1.768871462 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0625' to each side of the equation. 0.0625 + -0.0625 + x = 1.768871462 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + x = 1.768871462 + -0.0625 x = 1.768871462 + -0.0625 Combine like terms: 1.768871462 + -0.0625 = 1.706371462 x = 1.706371462 Simplifying x = 1.706371462Subproblem 2
x + 0.0625 = -1.768871462 Simplifying x + 0.0625 = -1.768871462 Reorder the terms: 0.0625 + x = -1.768871462 Solving 0.0625 + x = -1.768871462 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0625' to each side of the equation. 0.0625 + -0.0625 + x = -1.768871462 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + x = -1.768871462 + -0.0625 x = -1.768871462 + -0.0625 Combine like terms: -1.768871462 + -0.0625 = -1.831371462 x = -1.831371462 Simplifying x = -1.831371462Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.706371462, -1.831371462}
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