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Simplifying 5x2 + 50x + -28 = 0 Reorder the terms: -28 + 50x + 5x2 = 0 Solving -28 + 50x + 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'. -5.6 + 10x + x2 = 0 Move the constant term to the right: Add '5.6' to each side of the equation. -5.6 + 10x + 5.6 + x2 = 0 + 5.6 Reorder the terms: -5.6 + 5.6 + 10x + x2 = 0 + 5.6 Combine like terms: -5.6 + 5.6 = 0.0 0.0 + 10x + x2 = 0 + 5.6 10x + x2 = 0 + 5.6 Combine like terms: 0 + 5.6 = 5.6 10x + x2 = 5.6 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 5.6 + 25 Reorder the terms: 25 + 10x + x2 = 5.6 + 25 Combine like terms: 5.6 + 25 = 30.6 25 + 10x + x2 = 30.6 Factor a perfect square on the left side: (x + 5)(x + 5) = 30.6 Calculate the square root of the right side: 5.531726674 Break this problem into two subproblems by setting (x + 5) equal to 5.531726674 and -5.531726674.Subproblem 1
x + 5 = 5.531726674 Simplifying x + 5 = 5.531726674 Reorder the terms: 5 + x = 5.531726674 Solving 5 + x = 5.531726674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 5.531726674 + -5 Combine like terms: 5 + -5 = 0 0 + x = 5.531726674 + -5 x = 5.531726674 + -5 Combine like terms: 5.531726674 + -5 = 0.531726674 x = 0.531726674 Simplifying x = 0.531726674Subproblem 2
x + 5 = -5.531726674 Simplifying x + 5 = -5.531726674 Reorder the terms: 5 + x = -5.531726674 Solving 5 + x = -5.531726674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -5.531726674 + -5 Combine like terms: 5 + -5 = 0 0 + x = -5.531726674 + -5 x = -5.531726674 + -5 Combine like terms: -5.531726674 + -5 = -10.531726674 x = -10.531726674 Simplifying x = -10.531726674Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.531726674, -10.531726674}
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