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Simplifying 2(2x + -0.1) * 2x = 28.6 Reorder the terms: 2(-0.1 + 2x) * 2x = 28.6 Reorder the terms for easier multiplication: 2 * 2x(-0.1 + 2x) = 28.6 Multiply 2 * 2 4x(-0.1 + 2x) = 28.6 (-0.1 * 4x + 2x * 4x) = 28.6 (-0.4x + 8x2) = 28.6 Solving -0.4x + 8x2 = 28.6 Solving for variable 'x'. Reorder the terms: -28.6 + -0.4x + 8x2 = 28.6 + -28.6 Combine like terms: 28.6 + -28.6 = 0.0 -28.6 + -0.4x + 8x2 = 0.0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -3.575 + -0.05x + x2 = 0.0 Move the constant term to the right: Add '3.575' to each side of the equation. -3.575 + -0.05x + 3.575 + x2 = 0.0 + 3.575 Reorder the terms: -3.575 + 3.575 + -0.05x + x2 = 0.0 + 3.575 Combine like terms: -3.575 + 3.575 = 0.000 0.000 + -0.05x + x2 = 0.0 + 3.575 -0.05x + x2 = 0.0 + 3.575 Combine like terms: 0.0 + 3.575 = 3.575 -0.05x + x2 = 3.575 The x term is -0.05x. Take half its coefficient (-0.025). Square it (0.000625) and add it to both sides. Add '0.000625' to each side of the equation. -0.05x + 0.000625 + x2 = 3.575 + 0.000625 Reorder the terms: 0.000625 + -0.05x + x2 = 3.575 + 0.000625 Combine like terms: 3.575 + 0.000625 = 3.575625 0.000625 + -0.05x + x2 = 3.575625 Factor a perfect square on the left side: (x + -0.025)(x + -0.025) = 3.575625 Calculate the square root of the right side: 1.89093231 Break this problem into two subproblems by setting (x + -0.025) equal to 1.89093231 and -1.89093231.Subproblem 1
x + -0.025 = 1.89093231 Simplifying x + -0.025 = 1.89093231 Reorder the terms: -0.025 + x = 1.89093231 Solving -0.025 + x = 1.89093231 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.025' to each side of the equation. -0.025 + 0.025 + x = 1.89093231 + 0.025 Combine like terms: -0.025 + 0.025 = 0.000 0.000 + x = 1.89093231 + 0.025 x = 1.89093231 + 0.025 Combine like terms: 1.89093231 + 0.025 = 1.91593231 x = 1.91593231 Simplifying x = 1.91593231Subproblem 2
x + -0.025 = -1.89093231 Simplifying x + -0.025 = -1.89093231 Reorder the terms: -0.025 + x = -1.89093231 Solving -0.025 + x = -1.89093231 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.025' to each side of the equation. -0.025 + 0.025 + x = -1.89093231 + 0.025 Combine like terms: -0.025 + 0.025 = 0.000 0.000 + x = -1.89093231 + 0.025 x = -1.89093231 + 0.025 Combine like terms: -1.89093231 + 0.025 = -1.86593231 x = -1.86593231 Simplifying x = -1.86593231Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.91593231, -1.86593231}
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