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Simplifying 8x2 + 0.5x = 0.09 Reorder the terms: 0.5x + 8x2 = 0.09 Solving 0.5x + 8x2 = 0.09 Solving for variable 'x'. Reorder the terms: -0.09 + 0.5x + 8x2 = 0.09 + -0.09 Combine like terms: 0.09 + -0.09 = 0.00 -0.09 + 0.5x + 8x2 = 0.00 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.01125 + 0.0625x + x2 = 0.00 Move the constant term to the right: Add '0.01125' to each side of the equation. -0.01125 + 0.0625x + 0.01125 + x2 = 0.00 + 0.01125 Reorder the terms: -0.01125 + 0.01125 + 0.0625x + x2 = 0.00 + 0.01125 Combine like terms: -0.01125 + 0.01125 = 0.00000 0.00000 + 0.0625x + x2 = 0.00 + 0.01125 0.0625x + x2 = 0.00 + 0.01125 Combine like terms: 0.00 + 0.01125 = 0.01125 0.0625x + x2 = 0.01125 The x term is 0.0625x. Take half its coefficient (0.03125). Square it (0.0009765625) and add it to both sides. Add '0.0009765625' to each side of the equation. 0.0625x + 0.0009765625 + x2 = 0.01125 + 0.0009765625 Reorder the terms: 0.0009765625 + 0.0625x + x2 = 0.01125 + 0.0009765625 Combine like terms: 0.01125 + 0.0009765625 = 0.0122265625 0.0009765625 + 0.0625x + x2 = 0.0122265625 Factor a perfect square on the left side: (x + 0.03125)(x + 0.03125) = 0.0122265625 Calculate the square root of the right side: 0.110573788 Break this problem into two subproblems by setting (x + 0.03125) equal to 0.110573788 and -0.110573788.Subproblem 1
x + 0.03125 = 0.110573788 Simplifying x + 0.03125 = 0.110573788 Reorder the terms: 0.03125 + x = 0.110573788 Solving 0.03125 + x = 0.110573788 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.03125' to each side of the equation. 0.03125 + -0.03125 + x = 0.110573788 + -0.03125 Combine like terms: 0.03125 + -0.03125 = 0.00000 0.00000 + x = 0.110573788 + -0.03125 x = 0.110573788 + -0.03125 Combine like terms: 0.110573788 + -0.03125 = 0.079323788 x = 0.079323788 Simplifying x = 0.079323788Subproblem 2
x + 0.03125 = -0.110573788 Simplifying x + 0.03125 = -0.110573788 Reorder the terms: 0.03125 + x = -0.110573788 Solving 0.03125 + x = -0.110573788 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.03125' to each side of the equation. 0.03125 + -0.03125 + x = -0.110573788 + -0.03125 Combine like terms: 0.03125 + -0.03125 = 0.00000 0.00000 + x = -0.110573788 + -0.03125 x = -0.110573788 + -0.03125 Combine like terms: -0.110573788 + -0.03125 = -0.141823788 x = -0.141823788 Simplifying x = -0.141823788Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.079323788, -0.141823788}
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