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Simplifying 50x2 + 20x + -21 = 0 Reorder the terms: -21 + 20x + 50x2 = 0 Solving -21 + 20x + 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'. -0.42 + 0.4x + x2 = 0 Move the constant term to the right: Add '0.42' to each side of the equation. -0.42 + 0.4x + 0.42 + x2 = 0 + 0.42 Reorder the terms: -0.42 + 0.42 + 0.4x + x2 = 0 + 0.42 Combine like terms: -0.42 + 0.42 = 0.00 0.00 + 0.4x + x2 = 0 + 0.42 0.4x + x2 = 0 + 0.42 Combine like terms: 0 + 0.42 = 0.42 0.4x + x2 = 0.42 The x term is 0.4x. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4x + 0.04 + x2 = 0.42 + 0.04 Reorder the terms: 0.04 + 0.4x + x2 = 0.42 + 0.04 Combine like terms: 0.42 + 0.04 = 0.46 0.04 + 0.4x + x2 = 0.46 Factor a perfect square on the left side: (x + 0.2)(x + 0.2) = 0.46 Calculate the square root of the right side: 0.678232998 Break this problem into two subproblems by setting (x + 0.2) equal to 0.678232998 and -0.678232998.Subproblem 1
x + 0.2 = 0.678232998 Simplifying x + 0.2 = 0.678232998 Reorder the terms: 0.2 + x = 0.678232998 Solving 0.2 + x = 0.678232998 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = 0.678232998 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 0.678232998 + -0.2 x = 0.678232998 + -0.2 Combine like terms: 0.678232998 + -0.2 = 0.478232998 x = 0.478232998 Simplifying x = 0.478232998Subproblem 2
x + 0.2 = -0.678232998 Simplifying x + 0.2 = -0.678232998 Reorder the terms: 0.2 + x = -0.678232998 Solving 0.2 + x = -0.678232998 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = -0.678232998 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -0.678232998 + -0.2 x = -0.678232998 + -0.2 Combine like terms: -0.678232998 + -0.2 = -0.878232998 x = -0.878232998 Simplifying x = -0.878232998Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.478232998, -0.878232998}
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