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Simplifying 10x2 + 50x = 69 Reorder the terms: 50x + 10x2 = 69 Solving 50x + 10x2 = 69 Solving for variable 'x'. Reorder the terms: -69 + 50x + 10x2 = 69 + -69 Combine like terms: 69 + -69 = 0 -69 + 50x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -6.9 + 5x + x2 = 0 Move the constant term to the right: Add '6.9' to each side of the equation. -6.9 + 5x + 6.9 + x2 = 0 + 6.9 Reorder the terms: -6.9 + 6.9 + 5x + x2 = 0 + 6.9 Combine like terms: -6.9 + 6.9 = 0.0 0.0 + 5x + x2 = 0 + 6.9 5x + x2 = 0 + 6.9 Combine like terms: 0 + 6.9 = 6.9 5x + x2 = 6.9 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 6.9 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 6.9 + 6.25 Combine like terms: 6.9 + 6.25 = 13.15 6.25 + 5x + x2 = 13.15 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 13.15 Calculate the square root of the right side: 3.626292873 Break this problem into two subproblems by setting (x + 2.5) equal to 3.626292873 and -3.626292873.Subproblem 1
x + 2.5 = 3.626292873 Simplifying x + 2.5 = 3.626292873 Reorder the terms: 2.5 + x = 3.626292873 Solving 2.5 + x = 3.626292873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 3.626292873 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 3.626292873 + -2.5 x = 3.626292873 + -2.5 Combine like terms: 3.626292873 + -2.5 = 1.126292873 x = 1.126292873 Simplifying x = 1.126292873Subproblem 2
x + 2.5 = -3.626292873 Simplifying x + 2.5 = -3.626292873 Reorder the terms: 2.5 + x = -3.626292873 Solving 2.5 + x = -3.626292873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -3.626292873 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -3.626292873 + -2.5 x = -3.626292873 + -2.5 Combine like terms: -3.626292873 + -2.5 = -6.126292873 x = -6.126292873 Simplifying x = -6.126292873Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.126292873, -6.126292873}
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