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Simplifying 5x2 + 18x + -50 = 0 Reorder the terms: -50 + 18x + 5x2 = 0 Solving -50 + 18x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -10 + 3.6x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + 3.6x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + 3.6x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 3.6x + x2 = 0 + 10 3.6x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 3.6x + x2 = 10 The x term is 3.6x. Take half its coefficient (1.8). Square it (3.24) and add it to both sides. Add '3.24' to each side of the equation. 3.6x + 3.24 + x2 = 10 + 3.24 Reorder the terms: 3.24 + 3.6x + x2 = 10 + 3.24 Combine like terms: 10 + 3.24 = 13.24 3.24 + 3.6x + x2 = 13.24 Factor a perfect square on the left side: (x + 1.8)(x + 1.8) = 13.24 Calculate the square root of the right side: 3.63868108 Break this problem into two subproblems by setting (x + 1.8) equal to 3.63868108 and -3.63868108.Subproblem 1
x + 1.8 = 3.63868108 Simplifying x + 1.8 = 3.63868108 Reorder the terms: 1.8 + x = 3.63868108 Solving 1.8 + x = 3.63868108 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.8' to each side of the equation. 1.8 + -1.8 + x = 3.63868108 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + x = 3.63868108 + -1.8 x = 3.63868108 + -1.8 Combine like terms: 3.63868108 + -1.8 = 1.83868108 x = 1.83868108 Simplifying x = 1.83868108Subproblem 2
x + 1.8 = -3.63868108 Simplifying x + 1.8 = -3.63868108 Reorder the terms: 1.8 + x = -3.63868108 Solving 1.8 + x = -3.63868108 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.8' to each side of the equation. 1.8 + -1.8 + x = -3.63868108 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + x = -3.63868108 + -1.8 x = -3.63868108 + -1.8 Combine like terms: -3.63868108 + -1.8 = -5.43868108 x = -5.43868108 Simplifying x = -5.43868108Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.83868108, -5.43868108}
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