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Simplifying 5x2 + 5x = 254 Reorder the terms: 5x + 5x2 = 254 Solving 5x + 5x2 = 254 Solving for variable 'x'. Reorder the terms: -254 + 5x + 5x2 = 254 + -254 Combine like terms: 254 + -254 = 0 -254 + 5x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -50.8 + x + x2 = 0 Move the constant term to the right: Add '50.8' to each side of the equation. -50.8 + x + 50.8 + x2 = 0 + 50.8 Reorder the terms: -50.8 + 50.8 + x + x2 = 0 + 50.8 Combine like terms: -50.8 + 50.8 = 0.0 0.0 + x + x2 = 0 + 50.8 x + x2 = 0 + 50.8 Combine like terms: 0 + 50.8 = 50.8 x + x2 = 50.8 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 = 50.8 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 50.8 + 0.25 Combine like terms: 50.8 + 0.25 = 51.05 1.25 + x2 = 51.05 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 51.05 Calculate the square root of the right side: 7.144928271 Break this problem into two subproblems by setting (x + 0.5) equal to 7.144928271 and -7.144928271.Subproblem 1
x + 0.5 = 7.144928271 Simplifying x + 0.5 = 7.144928271 Reorder the terms: 0.5 + x = 7.144928271 Solving 0.5 + x = 7.144928271 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 = 7.144928271 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 7.144928271 + -0.5 x = 7.144928271 + -0.5 Combine like terms: 7.144928271 + -0.5 = 6.644928271 x = 6.644928271 Simplifying x = 6.644928271Subproblem 2
x + 0.5 = -7.144928271 Simplifying x + 0.5 = -7.144928271 Reorder the terms: 0.5 + x = -7.144928271 Solving 0.5 + x = -7.144928271 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 = -7.144928271 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -7.144928271 + -0.5 x = -7.144928271 + -0.5 Combine like terms: -7.144928271 + -0.5 = -7.644928271 x = -7.644928271 Simplifying x = -7.644928271Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.644928271, -7.644928271}
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