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Simplifying 5x2 + 30x + 2 = 0 Reorder the terms: 2 + 30x + 5x2 = 0 Solving 2 + 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'. 0.4 + 6x + x2 = 0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + 6x + -0.4 + x2 = 0 + -0.4 Reorder the terms: 0.4 + -0.4 + 6x + x2 = 0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + 6x + x2 = 0 + -0.4 6x + x2 = 0 + -0.4 Combine like terms: 0 + -0.4 = -0.4 6x + x2 = -0.4 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 = -0.4 + 9 Reorder the terms: 9 + 6x + x2 = -0.4 + 9 Combine like terms: -0.4 + 9 = 8.6 9 + 6x + x2 = 8.6 Factor a perfect square on the left side: (x + 3)(x + 3) = 8.6 Calculate the square root of the right side: 2.93257566 Break this problem into two subproblems by setting (x + 3) equal to 2.93257566 and -2.93257566.Subproblem 1
x + 3 = 2.93257566 Simplifying x + 3 = 2.93257566 Reorder the terms: 3 + x = 2.93257566 Solving 3 + x = 2.93257566 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 = 2.93257566 + -3 Combine like terms: 3 + -3 = 0 0 + x = 2.93257566 + -3 x = 2.93257566 + -3 Combine like terms: 2.93257566 + -3 = -0.06742434 x = -0.06742434 Simplifying x = -0.06742434Subproblem 2
x + 3 = -2.93257566 Simplifying x + 3 = -2.93257566 Reorder the terms: 3 + x = -2.93257566 Solving 3 + x = -2.93257566 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 = -2.93257566 + -3 Combine like terms: 3 + -3 = 0 0 + x = -2.93257566 + -3 x = -2.93257566 + -3 Combine like terms: -2.93257566 + -3 = -5.93257566 x = -5.93257566 Simplifying x = -5.93257566Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.06742434, -5.93257566}
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