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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 = 19.4 25 + 10x + x2 = 19.4 Factor a perfect square on the left side: (x + 5)(x + 5) = 19.4 Calculate the square root of the right side: 4.404543109 Break this problem into two subproblems by setting (x + 5) equal to 4.404543109 and -4.404543109.Subproblem 1
x + 5 = 4.404543109 Simplifying x + 5 = 4.404543109 Reorder the terms: 5 + x = 4.404543109 Solving 5 + x = 4.404543109 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 = 4.404543109 + -5 Combine like terms: 5 + -5 = 0 0 + x = 4.404543109 + -5 x = 4.404543109 + -5 Combine like terms: 4.404543109 + -5 = -0.595456891 x = -0.595456891 Simplifying x = -0.595456891Subproblem 2
x + 5 = -4.404543109 Simplifying x + 5 = -4.404543109 Reorder the terms: 5 + x = -4.404543109 Solving 5 + x = -4.404543109 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 = -4.404543109 + -5 Combine like terms: 5 + -5 = 0 0 + x = -4.404543109 + -5 x = -4.404543109 + -5 Combine like terms: -4.404543109 + -5 = -9.404543109 x = -9.404543109 Simplifying x = -9.404543109Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.595456891, -9.404543109}
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