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Simplifying 5x2 + 30x + 4 = 0 Reorder the terms: 4 + 30x + 5x2 = 0 Solving 4 + 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'. 0.8 + 6x + x2 = 0 Move the constant term to the right: Add '-0.8' to each side of the equation. 0.8 + 6x + -0.8 + x2 = 0 + -0.8 Reorder the terms: 0.8 + -0.8 + 6x + x2 = 0 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + 6x + x2 = 0 + -0.8 6x + x2 = 0 + -0.8 Combine like terms: 0 + -0.8 = -0.8 6x + x2 = -0.8 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 = -0.8 + 9 Reorder the terms: 9 + 6x + x2 = -0.8 + 9 Combine like terms: -0.8 + 9 = 8.2 9 + 6x + x2 = 8.2 Factor a perfect square on the left side: (x + 3)(x + 3) = 8.2 Calculate the square root of the right side: 2.863564213 Break this problem into two subproblems by setting (x + 3) equal to 2.863564213 and -2.863564213.Subproblem 1
x + 3 = 2.863564213 Simplifying x + 3 = 2.863564213 Reorder the terms: 3 + x = 2.863564213 Solving 3 + x = 2.863564213 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 = 2.863564213 + -3 Combine like terms: 3 + -3 = 0 0 + x = 2.863564213 + -3 x = 2.863564213 + -3 Combine like terms: 2.863564213 + -3 = -0.136435787 x = -0.136435787 Simplifying x = -0.136435787Subproblem 2
x + 3 = -2.863564213 Simplifying x + 3 = -2.863564213 Reorder the terms: 3 + x = -2.863564213 Solving 3 + x = -2.863564213 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 = -2.863564213 + -3 Combine like terms: 3 + -3 = 0 0 + x = -2.863564213 + -3 x = -2.863564213 + -3 Combine like terms: -2.863564213 + -3 = -5.863564213 x = -5.863564213 Simplifying x = -5.863564213Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.136435787, -5.863564213}
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