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Simplifying 20x2 + 5.2x + -0.5 = 0 Reorder the terms: -0.5 + 5.2x + 20x2 = 0 Solving -0.5 + 5.2x + 20x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -0.025 + 0.26x + x2 = 0 Move the constant term to the right: Add '0.025' to each side of the equation. -0.025 + 0.26x + 0.025 + x2 = 0 + 0.025 Reorder the terms: -0.025 + 0.025 + 0.26x + x2 = 0 + 0.025 Combine like terms: -0.025 + 0.025 = 0.000 0.000 + 0.26x + x2 = 0 + 0.025 0.26x + x2 = 0 + 0.025 Combine like terms: 0 + 0.025 = 0.025 0.26x + x2 = 0.025 The x term is 0.26x. Take half its coefficient (0.13). Square it (0.0169) and add it to both sides. Add '0.0169' to each side of the equation. 0.26x + 0.0169 + x2 = 0.025 + 0.0169 Reorder the terms: 0.0169 + 0.26x + x2 = 0.025 + 0.0169 Combine like terms: 0.025 + 0.0169 = 0.0419 0.0169 + 0.26x + x2 = 0.0419 Factor a perfect square on the left side: (x + 0.13)(x + 0.13) = 0.0419 Calculate the square root of the right side: 0.204694895 Break this problem into two subproblems by setting (x + 0.13) equal to 0.204694895 and -0.204694895.Subproblem 1
x + 0.13 = 0.204694895 Simplifying x + 0.13 = 0.204694895 Reorder the terms: 0.13 + x = 0.204694895 Solving 0.13 + x = 0.204694895 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.13' to each side of the equation. 0.13 + -0.13 + x = 0.204694895 + -0.13 Combine like terms: 0.13 + -0.13 = 0.00 0.00 + x = 0.204694895 + -0.13 x = 0.204694895 + -0.13 Combine like terms: 0.204694895 + -0.13 = 0.074694895 x = 0.074694895 Simplifying x = 0.074694895Subproblem 2
x + 0.13 = -0.204694895 Simplifying x + 0.13 = -0.204694895 Reorder the terms: 0.13 + x = -0.204694895 Solving 0.13 + x = -0.204694895 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.13' to each side of the equation. 0.13 + -0.13 + x = -0.204694895 + -0.13 Combine like terms: 0.13 + -0.13 = 0.00 0.00 + x = -0.204694895 + -0.13 x = -0.204694895 + -0.13 Combine like terms: -0.204694895 + -0.13 = -0.334694895 x = -0.334694895 Simplifying x = -0.334694895Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.074694895, -0.334694895}
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