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Simplifying 8x2 = x + 100 Reorder the terms: 8x2 = 100 + x Solving 8x2 = 100 + x Solving for variable 'x'. Reorder the terms: -100 + -1x + 8x2 = 100 + x + -100 + -1x Reorder the terms: -100 + -1x + 8x2 = 100 + -100 + x + -1x Combine like terms: 100 + -100 = 0 -100 + -1x + 8x2 = 0 + x + -1x -100 + -1x + 8x2 = x + -1x Combine like terms: x + -1x = 0 -100 + -1x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -12.5 + -0.125x + x2 = 0 Move the constant term to the right: Add '12.5' to each side of the equation. -12.5 + -0.125x + 12.5 + x2 = 0 + 12.5 Reorder the terms: -12.5 + 12.5 + -0.125x + x2 = 0 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + -0.125x + x2 = 0 + 12.5 -0.125x + x2 = 0 + 12.5 Combine like terms: 0 + 12.5 = 12.5 -0.125x + x2 = 12.5 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 = 12.5 + 0.00390625 Reorder the terms: 0.00390625 + -0.125x + x2 = 12.5 + 0.00390625 Combine like terms: 12.5 + 0.00390625 = 12.50390625 0.00390625 + -0.125x + x2 = 12.50390625 Factor a perfect square on the left side: (x + -0.0625)(x + -0.0625) = 12.50390625 Calculate the square root of the right side: 3.53608629 Break this problem into two subproblems by setting (x + -0.0625) equal to 3.53608629 and -3.53608629.Subproblem 1
x + -0.0625 = 3.53608629 Simplifying x + -0.0625 = 3.53608629 Reorder the terms: -0.0625 + x = 3.53608629 Solving -0.0625 + x = 3.53608629 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 = 3.53608629 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + x = 3.53608629 + 0.0625 x = 3.53608629 + 0.0625 Combine like terms: 3.53608629 + 0.0625 = 3.59858629 x = 3.59858629 Simplifying x = 3.59858629Subproblem 2
x + -0.0625 = -3.53608629 Simplifying x + -0.0625 = -3.53608629 Reorder the terms: -0.0625 + x = -3.53608629 Solving -0.0625 + x = -3.53608629 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 = -3.53608629 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + x = -3.53608629 + 0.0625 x = -3.53608629 + 0.0625 Combine like terms: -3.53608629 + 0.0625 = -3.47358629 x = -3.47358629 Simplifying x = -3.47358629Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.59858629, -3.47358629}
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