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Simplifying 5x2 + 30x + 39 = 0 Reorder the terms: 39 + 30x + 5x2 = 0 Solving 39 + 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'. 7.8 + 6x + x2 = 0 Move the constant term to the right: Add '-7.8' to each side of the equation. 7.8 + 6x + -7.8 + x2 = 0 + -7.8 Reorder the terms: 7.8 + -7.8 + 6x + x2 = 0 + -7.8 Combine like terms: 7.8 + -7.8 = 0.0 0.0 + 6x + x2 = 0 + -7.8 6x + x2 = 0 + -7.8 Combine like terms: 0 + -7.8 = -7.8 6x + x2 = -7.8 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 = -7.8 + 9 Reorder the terms: 9 + 6x + x2 = -7.8 + 9 Combine like terms: -7.8 + 9 = 1.2 9 + 6x + x2 = 1.2 Factor a perfect square on the left side: (x + 3)(x + 3) = 1.2 Calculate the square root of the right side: 1.095445115 Break this problem into two subproblems by setting (x + 3) equal to 1.095445115 and -1.095445115.Subproblem 1
x + 3 = 1.095445115 Simplifying x + 3 = 1.095445115 Reorder the terms: 3 + x = 1.095445115 Solving 3 + x = 1.095445115 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 = 1.095445115 + -3 Combine like terms: 3 + -3 = 0 0 + x = 1.095445115 + -3 x = 1.095445115 + -3 Combine like terms: 1.095445115 + -3 = -1.904554885 x = -1.904554885 Simplifying x = -1.904554885Subproblem 2
x + 3 = -1.095445115 Simplifying x + 3 = -1.095445115 Reorder the terms: 3 + x = -1.095445115 Solving 3 + x = -1.095445115 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 = -1.095445115 + -3 Combine like terms: 3 + -3 = 0 0 + x = -1.095445115 + -3 x = -1.095445115 + -3 Combine like terms: -1.095445115 + -3 = -4.095445115 x = -4.095445115 Simplifying x = -4.095445115Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.904554885, -4.095445115}
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