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Simplifying 8x2 + 81x + -3 = 0 Reorder the terms: -3 + 81x + 8x2 = 0 Solving -3 + 81x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.375 + 10.125x + x2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + 10.125x + 0.375 + x2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + 10.125x + x2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + 10.125x + x2 = 0 + 0.375 10.125x + x2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 10.125x + x2 = 0.375 The x term is 10.125x. Take half its coefficient (5.0625). Square it (25.62890625) and add it to both sides. Add '25.62890625' to each side of the equation. 10.125x + 25.62890625 + x2 = 0.375 + 25.62890625 Reorder the terms: 25.62890625 + 10.125x + x2 = 0.375 + 25.62890625 Combine like terms: 0.375 + 25.62890625 = 26.00390625 25.62890625 + 10.125x + x2 = 26.00390625 Factor a perfect square on the left side: (x + 5.0625)(x + 5.0625) = 26.00390625 Calculate the square root of the right side: 5.099402539 Break this problem into two subproblems by setting (x + 5.0625) equal to 5.099402539 and -5.099402539.Subproblem 1
x + 5.0625 = 5.099402539 Simplifying x + 5.0625 = 5.099402539 Reorder the terms: 5.0625 + x = 5.099402539 Solving 5.0625 + x = 5.099402539 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.0625' to each side of the equation. 5.0625 + -5.0625 + x = 5.099402539 + -5.0625 Combine like terms: 5.0625 + -5.0625 = 0.0000 0.0000 + x = 5.099402539 + -5.0625 x = 5.099402539 + -5.0625 Combine like terms: 5.099402539 + -5.0625 = 0.036902539 x = 0.036902539 Simplifying x = 0.036902539Subproblem 2
x + 5.0625 = -5.099402539 Simplifying x + 5.0625 = -5.099402539 Reorder the terms: 5.0625 + x = -5.099402539 Solving 5.0625 + x = -5.099402539 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.0625' to each side of the equation. 5.0625 + -5.0625 + x = -5.099402539 + -5.0625 Combine like terms: 5.0625 + -5.0625 = 0.0000 0.0000 + x = -5.099402539 + -5.0625 x = -5.099402539 + -5.0625 Combine like terms: -5.099402539 + -5.0625 = -10.161902539 x = -10.161902539 Simplifying x = -10.161902539Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.036902539, -10.161902539}
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