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Simplifying 20x2 + 20x = 1 Reorder the terms: 20x + 20x2 = 1 Solving 20x + 20x2 = 1 Solving for variable 'x'. Reorder the terms: -1 + 20x + 20x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + 20x + 20x2 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -0.05 + x + x2 = 0 Move the constant term to the right: Add '0.05' to each side of the equation. -0.05 + x + 0.05 + x2 = 0 + 0.05 Reorder the terms: -0.05 + 0.05 + x + x2 = 0 + 0.05 Combine like terms: -0.05 + 0.05 = 0.00 0.00 + x + x2 = 0 + 0.05 x + x2 = 0 + 0.05 Combine like terms: 0 + 0.05 = 0.05 x + x2 = 0.05 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 0.05 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 0.05 + 0.25 Combine like terms: 0.05 + 0.25 = 0.3 1.25 + x2 = 0.3 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.3 Calculate the square root of the right side: 0.547722558 Break this problem into two subproblems by setting (x + 0.5) equal to 0.547722558 and -0.547722558.Subproblem 1
x + 0.5 = 0.547722558 Simplifying x + 0.5 = 0.547722558 Reorder the terms: 0.5 + x = 0.547722558 Solving 0.5 + x = 0.547722558 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 0.547722558 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.547722558 + -0.5 x = 0.547722558 + -0.5 Combine like terms: 0.547722558 + -0.5 = 0.047722558 x = 0.047722558 Simplifying x = 0.047722558Subproblem 2
x + 0.5 = -0.547722558 Simplifying x + 0.5 = -0.547722558 Reorder the terms: 0.5 + x = -0.547722558 Solving 0.5 + x = -0.547722558 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -0.547722558 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.547722558 + -0.5 x = -0.547722558 + -0.5 Combine like terms: -0.547722558 + -0.5 = -1.047722558 x = -1.047722558 Simplifying x = -1.047722558Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.047722558, -1.047722558}
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