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Simplifying 8x2 + 1 = 10x Reorder the terms: 1 + 8x2 = 10x Solving 1 + 8x2 = 10x Solving for variable 'x'. Reorder the terms: 1 + -10x + 8x2 = 10x + -10x Combine like terms: 10x + -10x = 0 1 + -10x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.125 + -1.25x + x2 = 0 Move the constant term to the right: Add '-0.125' to each side of the equation. 0.125 + -1.25x + -0.125 + x2 = 0 + -0.125 Reorder the terms: 0.125 + -0.125 + -1.25x + x2 = 0 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + -1.25x + x2 = 0 + -0.125 -1.25x + x2 = 0 + -0.125 Combine like terms: 0 + -0.125 = -0.125 -1.25x + x2 = -0.125 The x term is -1.25x. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25x + 0.390625 + x2 = -0.125 + 0.390625 Reorder the terms: 0.390625 + -1.25x + x2 = -0.125 + 0.390625 Combine like terms: -0.125 + 0.390625 = 0.265625 0.390625 + -1.25x + x2 = 0.265625 Factor a perfect square on the left side: (x + -0.625)(x + -0.625) = 0.265625 Calculate the square root of the right side: 0.515388203 Break this problem into two subproblems by setting (x + -0.625) equal to 0.515388203 and -0.515388203.Subproblem 1
x + -0.625 = 0.515388203 Simplifying x + -0.625 = 0.515388203 Reorder the terms: -0.625 + x = 0.515388203 Solving -0.625 + x = 0.515388203 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = 0.515388203 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = 0.515388203 + 0.625 x = 0.515388203 + 0.625 Combine like terms: 0.515388203 + 0.625 = 1.140388203 x = 1.140388203 Simplifying x = 1.140388203Subproblem 2
x + -0.625 = -0.515388203 Simplifying x + -0.625 = -0.515388203 Reorder the terms: -0.625 + x = -0.515388203 Solving -0.625 + x = -0.515388203 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = -0.515388203 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = -0.515388203 + 0.625 x = -0.515388203 + 0.625 Combine like terms: -0.515388203 + 0.625 = 0.109611797 x = 0.109611797 Simplifying x = 0.109611797Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.140388203, 0.109611797}
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