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Simplifying 100x2 + -3.2x + -0.1805 = 0 Reorder the terms: -0.1805 + -3.2x + 100x2 = 0 Solving -0.1805 + -3.2x + 100x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 100 the coefficient of the squared term: Divide each side by '100'. -0.001805 + -0.032x + x2 = 0 Move the constant term to the right: Add '0.001805' to each side of the equation. -0.001805 + -0.032x + 0.001805 + x2 = 0 + 0.001805 Reorder the terms: -0.001805 + 0.001805 + -0.032x + x2 = 0 + 0.001805 Combine like terms: -0.001805 + 0.001805 = 0.000000 0.000000 + -0.032x + x2 = 0 + 0.001805 -0.032x + x2 = 0 + 0.001805 Combine like terms: 0 + 0.001805 = 0.001805 -0.032x + x2 = 0.001805 The x term is -0.032x. Take half its coefficient (-0.016). Square it (0.000256) and add it to both sides. Add '0.000256' to each side of the equation. -0.032x + 0.000256 + x2 = 0.001805 + 0.000256 Reorder the terms: 0.000256 + -0.032x + x2 = 0.001805 + 0.000256 Combine like terms: 0.001805 + 0.000256 = 0.002061 0.000256 + -0.032x + x2 = 0.002061 Factor a perfect square on the left side: (x + -0.016)(x + -0.016) = 0.002061 Calculate the square root of the right side: 0.045398238 Break this problem into two subproblems by setting (x + -0.016) equal to 0.045398238 and -0.045398238.Subproblem 1
x + -0.016 = 0.045398238 Simplifying x + -0.016 = 0.045398238 Reorder the terms: -0.016 + x = 0.045398238 Solving -0.016 + x = 0.045398238 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.016' to each side of the equation. -0.016 + 0.016 + x = 0.045398238 + 0.016 Combine like terms: -0.016 + 0.016 = 0.000 0.000 + x = 0.045398238 + 0.016 x = 0.045398238 + 0.016 Combine like terms: 0.045398238 + 0.016 = 0.061398238 x = 0.061398238 Simplifying x = 0.061398238Subproblem 2
x + -0.016 = -0.045398238 Simplifying x + -0.016 = -0.045398238 Reorder the terms: -0.016 + x = -0.045398238 Solving -0.016 + x = -0.045398238 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.016' to each side of the equation. -0.016 + 0.016 + x = -0.045398238 + 0.016 Combine like terms: -0.016 + 0.016 = 0.000 0.000 + x = -0.045398238 + 0.016 x = -0.045398238 + 0.016 Combine like terms: -0.045398238 + 0.016 = -0.029398238 x = -0.029398238 Simplifying x = -0.029398238Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.061398238, -0.029398238}
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