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Simplifying 50x2 + 10x + -1 = 0 Reorder the terms: -1 + 10x + 50x2 = 0 Solving -1 + 10x + 50x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 50 the coefficient of the squared term: Divide each side by '50'. -0.02 + 0.2x + x2 = 0 Move the constant term to the right: Add '0.02' to each side of the equation. -0.02 + 0.2x + 0.02 + x2 = 0 + 0.02 Reorder the terms: -0.02 + 0.02 + 0.2x + x2 = 0 + 0.02 Combine like terms: -0.02 + 0.02 = 0.00 0.00 + 0.2x + x2 = 0 + 0.02 0.2x + x2 = 0 + 0.02 Combine like terms: 0 + 0.02 = 0.02 0.2x + x2 = 0.02 The x term is 0.2x. Take half its coefficient (0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. 0.2x + 0.01 + x2 = 0.02 + 0.01 Reorder the terms: 0.01 + 0.2x + x2 = 0.02 + 0.01 Combine like terms: 0.02 + 0.01 = 0.03 0.01 + 0.2x + x2 = 0.03 Factor a perfect square on the left side: (x + 0.1)(x + 0.1) = 0.03 Calculate the square root of the right side: 0.173205081 Break this problem into two subproblems by setting (x + 0.1) equal to 0.173205081 and -0.173205081.Subproblem 1
x + 0.1 = 0.173205081 Simplifying x + 0.1 = 0.173205081 Reorder the terms: 0.1 + x = 0.173205081 Solving 0.1 + x = 0.173205081 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + x = 0.173205081 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = 0.173205081 + -0.1 x = 0.173205081 + -0.1 Combine like terms: 0.173205081 + -0.1 = 0.073205081 x = 0.073205081 Simplifying x = 0.073205081Subproblem 2
x + 0.1 = -0.173205081 Simplifying x + 0.1 = -0.173205081 Reorder the terms: 0.1 + x = -0.173205081 Solving 0.1 + x = -0.173205081 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + x = -0.173205081 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = -0.173205081 + -0.1 x = -0.173205081 + -0.1 Combine like terms: -0.173205081 + -0.1 = -0.273205081 x = -0.273205081 Simplifying x = -0.273205081Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.073205081, -0.273205081}
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