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Simplifying 5x2 + 49x + 39 = 0 Reorder the terms: 39 + 49x + 5x2 = 0 Solving 39 + 49x + 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 + 9.8x + x2 = 0 Move the constant term to the right: Add '-7.8' to each side of the equation. 7.8 + 9.8x + -7.8 + x2 = 0 + -7.8 Reorder the terms: 7.8 + -7.8 + 9.8x + x2 = 0 + -7.8 Combine like terms: 7.8 + -7.8 = 0.0 0.0 + 9.8x + x2 = 0 + -7.8 9.8x + x2 = 0 + -7.8 Combine like terms: 0 + -7.8 = -7.8 9.8x + x2 = -7.8 The x term is 9.8x. Take half its coefficient (4.9). Square it (24.01) and add it to both sides. Add '24.01' to each side of the equation. 9.8x + 24.01 + x2 = -7.8 + 24.01 Reorder the terms: 24.01 + 9.8x + x2 = -7.8 + 24.01 Combine like terms: -7.8 + 24.01 = 16.21 24.01 + 9.8x + x2 = 16.21 Factor a perfect square on the left side: (x + 4.9)(x + 4.9) = 16.21 Calculate the square root of the right side: 4.026164428 Break this problem into two subproblems by setting (x + 4.9) equal to 4.026164428 and -4.026164428.Subproblem 1
x + 4.9 = 4.026164428 Simplifying x + 4.9 = 4.026164428 Reorder the terms: 4.9 + x = 4.026164428 Solving 4.9 + x = 4.026164428 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.9' to each side of the equation. 4.9 + -4.9 + x = 4.026164428 + -4.9 Combine like terms: 4.9 + -4.9 = 0.0 0.0 + x = 4.026164428 + -4.9 x = 4.026164428 + -4.9 Combine like terms: 4.026164428 + -4.9 = -0.873835572 x = -0.873835572 Simplifying x = -0.873835572Subproblem 2
x + 4.9 = -4.026164428 Simplifying x + 4.9 = -4.026164428 Reorder the terms: 4.9 + x = -4.026164428 Solving 4.9 + x = -4.026164428 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.9' to each side of the equation. 4.9 + -4.9 + x = -4.026164428 + -4.9 Combine like terms: 4.9 + -4.9 = 0.0 0.0 + x = -4.026164428 + -4.9 x = -4.026164428 + -4.9 Combine like terms: -4.026164428 + -4.9 = -8.926164428 x = -8.926164428 Simplifying x = -8.926164428Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.873835572, -8.926164428}
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