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Simplifying 0.04x2 + x + -5.24 = 0 Reorder the terms: -5.24 + x + 0.04x2 = 0 Solving -5.24 + x + 0.04x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.04 the coefficient of the squared term: Divide each side by '0.04'. -131 + 25x + x2 = 0 Move the constant term to the right: Add '131' to each side of the equation. -131 + 25x + 131 + x2 = 0 + 131 Reorder the terms: -131 + 131 + 25x + x2 = 0 + 131 Combine like terms: -131 + 131 = 0 0 + 25x + x2 = 0 + 131 25x + x2 = 0 + 131 Combine like terms: 0 + 131 = 131 25x + x2 = 131 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. 25x + 0.25 + x2 = 131 + 0.25 Reorder the terms: 0.25 + 25x + x2 = 131 + 0.25 Combine like terms: 131 + 0.25 = 131.25 0.25 + 25x + x2 = 131.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 131.25 Calculate the square root of the right side: 11.456439237 Break this problem into two subproblems by setting (x + 0.5) equal to 11.456439237 and -11.456439237.Subproblem 1
x + 0.5 = 11.456439237 Simplifying x + 0.5 = 11.456439237 Reorder the terms: 0.5 + x = 11.456439237 Solving 0.5 + x = 11.456439237 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 = 11.456439237 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 11.456439237 + -0.5 x = 11.456439237 + -0.5 Combine like terms: 11.456439237 + -0.5 = 10.956439237 x = 10.956439237 Simplifying x = 10.956439237Subproblem 2
x + 0.5 = -11.456439237 Simplifying x + 0.5 = -11.456439237 Reorder the terms: 0.5 + x = -11.456439237 Solving 0.5 + x = -11.456439237 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 = -11.456439237 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -11.456439237 + -0.5 x = -11.456439237 + -0.5 Combine like terms: -11.456439237 + -0.5 = -11.956439237 x = -11.956439237 Simplifying x = -11.956439237Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.956439237, -11.956439237}
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