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Simplifying 5x2 + 30x + 28 = 0 Reorder the terms: 28 + 30x + 5x2 = 0 Solving 28 + 30x + 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 + 6x + x2 = 0 Move the constant term to the right: Add '-5.6' to each side of the equation. 5.6 + 6x + -5.6 + x2 = 0 + -5.6 Reorder the terms: 5.6 + -5.6 + 6x + x2 = 0 + -5.6 Combine like terms: 5.6 + -5.6 = 0.0 0.0 + 6x + x2 = 0 + -5.6 6x + x2 = 0 + -5.6 Combine like terms: 0 + -5.6 = -5.6 6x + x2 = -5.6 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = -5.6 + 9 Reorder the terms: 9 + 6x + x2 = -5.6 + 9 Combine like terms: -5.6 + 9 = 3.4 9 + 6x + x2 = 3.4 Factor a perfect square on the left side: (x + 3)(x + 3) = 3.4 Calculate the square root of the right side: 1.843908891 Break this problem into two subproblems by setting (x + 3) equal to 1.843908891 and -1.843908891.Subproblem 1
x + 3 = 1.843908891 Simplifying x + 3 = 1.843908891 Reorder the terms: 3 + x = 1.843908891 Solving 3 + x = 1.843908891 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 1.843908891 + -3 Combine like terms: 3 + -3 = 0 0 + x = 1.843908891 + -3 x = 1.843908891 + -3 Combine like terms: 1.843908891 + -3 = -1.156091109 x = -1.156091109 Simplifying x = -1.156091109Subproblem 2
x + 3 = -1.843908891 Simplifying x + 3 = -1.843908891 Reorder the terms: 3 + x = -1.843908891 Solving 3 + x = -1.843908891 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -1.843908891 + -3 Combine like terms: 3 + -3 = 0 0 + x = -1.843908891 + -3 x = -1.843908891 + -3 Combine like terms: -1.843908891 + -3 = -4.843908891 x = -4.843908891 Simplifying x = -4.843908891Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.156091109, -4.843908891}
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