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Simplifying 0.05x2 + x + -56.25 = 0 Reorder the terms: -56.25 + x + 0.05x2 = 0 Solving -56.25 + x + 0.05x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.05 the coefficient of the squared term: Divide each side by '0.05'. -1125 + 20x + x2 = 0 Move the constant term to the right: Add '1125' to each side of the equation. -1125 + 20x + 1125 + x2 = 0 + 1125 Reorder the terms: -1125 + 1125 + 20x + x2 = 0 + 1125 Combine like terms: -1125 + 1125 = 0 0 + 20x + x2 = 0 + 1125 20x + x2 = 0 + 1125 Combine like terms: 0 + 1125 = 1125 20x + x2 = 1125 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. 20x + 0.25 + x2 = 1125 + 0.25 Reorder the terms: 0.25 + 20x + x2 = 1125 + 0.25 Combine like terms: 1125 + 0.25 = 1125.25 0.25 + 20x + x2 = 1125.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 1125.25 Calculate the square root of the right side: 33.544746235 Break this problem into two subproblems by setting (x + 0.5) equal to 33.544746235 and -33.544746235.Subproblem 1
x + 0.5 = 33.544746235 Simplifying x + 0.5 = 33.544746235 Reorder the terms: 0.5 + x = 33.544746235 Solving 0.5 + x = 33.544746235 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 = 33.544746235 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 33.544746235 + -0.5 x = 33.544746235 + -0.5 Combine like terms: 33.544746235 + -0.5 = 33.044746235 x = 33.044746235 Simplifying x = 33.044746235Subproblem 2
x + 0.5 = -33.544746235 Simplifying x + 0.5 = -33.544746235 Reorder the terms: 0.5 + x = -33.544746235 Solving 0.5 + x = -33.544746235 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 = -33.544746235 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -33.544746235 + -0.5 x = -33.544746235 + -0.5 Combine like terms: -33.544746235 + -0.5 = -34.044746235 x = -34.044746235 Simplifying x = -34.044746235Solution
The solution to the problem is based on the solutions from the subproblems. x = {33.044746235, -34.044746235}
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