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Simplifying 8x2 + 0.9x = 0.06 Reorder the terms: 0.9x + 8x2 = 0.06 Solving 0.9x + 8x2 = 0.06 Solving for variable 'x'. Reorder the terms: -0.06 + 0.9x + 8x2 = 0.06 + -0.06 Combine like terms: 0.06 + -0.06 = 0.00 -0.06 + 0.9x + 8x2 = 0.00 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.0075 + 0.1125x + x2 = 0.00 Move the constant term to the right: Add '0.0075' to each side of the equation. -0.0075 + 0.1125x + 0.0075 + x2 = 0.00 + 0.0075 Reorder the terms: -0.0075 + 0.0075 + 0.1125x + x2 = 0.00 + 0.0075 Combine like terms: -0.0075 + 0.0075 = 0.0000 0.0000 + 0.1125x + x2 = 0.00 + 0.0075 0.1125x + x2 = 0.00 + 0.0075 Combine like terms: 0.00 + 0.0075 = 0.0075 0.1125x + x2 = 0.0075 The x term is 0.1125x. Take half its coefficient (0.05625). Square it (0.0031640625) and add it to both sides. Add '0.0031640625' to each side of the equation. 0.1125x + 0.0031640625 + x2 = 0.0075 + 0.0031640625 Reorder the terms: 0.0031640625 + 0.1125x + x2 = 0.0075 + 0.0031640625 Combine like terms: 0.0075 + 0.0031640625 = 0.0106640625 0.0031640625 + 0.1125x + x2 = 0.0106640625 Factor a perfect square on the left side: (x + 0.05625)(x + 0.05625) = 0.0106640625 Calculate the square root of the right side: 0.103266948 Break this problem into two subproblems by setting (x + 0.05625) equal to 0.103266948 and -0.103266948.Subproblem 1
x + 0.05625 = 0.103266948 Simplifying x + 0.05625 = 0.103266948 Reorder the terms: 0.05625 + x = 0.103266948 Solving 0.05625 + x = 0.103266948 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.05625' to each side of the equation. 0.05625 + -0.05625 + x = 0.103266948 + -0.05625 Combine like terms: 0.05625 + -0.05625 = 0.00000 0.00000 + x = 0.103266948 + -0.05625 x = 0.103266948 + -0.05625 Combine like terms: 0.103266948 + -0.05625 = 0.047016948 x = 0.047016948 Simplifying x = 0.047016948Subproblem 2
x + 0.05625 = -0.103266948 Simplifying x + 0.05625 = -0.103266948 Reorder the terms: 0.05625 + x = -0.103266948 Solving 0.05625 + x = -0.103266948 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.05625' to each side of the equation. 0.05625 + -0.05625 + x = -0.103266948 + -0.05625 Combine like terms: 0.05625 + -0.05625 = 0.00000 0.00000 + x = -0.103266948 + -0.05625 x = -0.103266948 + -0.05625 Combine like terms: -0.103266948 + -0.05625 = -0.159516948 x = -0.159516948 Simplifying x = -0.159516948Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.047016948, -0.159516948}
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