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Simplifying 49x2 + -395x + -30 = 0 Reorder the terms: -30 + -395x + 49x2 = 0 Solving -30 + -395x + 49x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. -0.612244898 + -8.06122449x + x2 = 0 Move the constant term to the right: Add '0.612244898' to each side of the equation. -0.612244898 + -8.06122449x + 0.612244898 + x2 = 0 + 0.612244898 Reorder the terms: -0.612244898 + 0.612244898 + -8.06122449x + x2 = 0 + 0.612244898 Combine like terms: -0.612244898 + 0.612244898 = 0.000000000 0.000000000 + -8.06122449x + x2 = 0 + 0.612244898 -8.06122449x + x2 = 0 + 0.612244898 Combine like terms: 0 + 0.612244898 = 0.612244898 -8.06122449x + x2 = 0.612244898 The x term is -8.06122449x. Take half its coefficient (-4.030612245). Square it (16.24583507) and add it to both sides. Add '16.24583507' to each side of the equation. -8.06122449x + 16.24583507 + x2 = 0.612244898 + 16.24583507 Reorder the terms: 16.24583507 + -8.06122449x + x2 = 0.612244898 + 16.24583507 Combine like terms: 0.612244898 + 16.24583507 = 16.858079968 16.24583507 + -8.06122449x + x2 = 16.858079968 Factor a perfect square on the left side: (x + -4.030612245)(x + -4.030612245) = 16.858079968 Calculate the square root of the right side: 4.105859224 Break this problem into two subproblems by setting (x + -4.030612245) equal to 4.105859224 and -4.105859224.Subproblem 1
x + -4.030612245 = 4.105859224 Simplifying x + -4.030612245 = 4.105859224 Reorder the terms: -4.030612245 + x = 4.105859224 Solving -4.030612245 + x = 4.105859224 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.030612245' to each side of the equation. -4.030612245 + 4.030612245 + x = 4.105859224 + 4.030612245 Combine like terms: -4.030612245 + 4.030612245 = 0.000000000 0.000000000 + x = 4.105859224 + 4.030612245 x = 4.105859224 + 4.030612245 Combine like terms: 4.105859224 + 4.030612245 = 8.136471469 x = 8.136471469 Simplifying x = 8.136471469Subproblem 2
x + -4.030612245 = -4.105859224 Simplifying x + -4.030612245 = -4.105859224 Reorder the terms: -4.030612245 + x = -4.105859224 Solving -4.030612245 + x = -4.105859224 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.030612245' to each side of the equation. -4.030612245 + 4.030612245 + x = -4.105859224 + 4.030612245 Combine like terms: -4.030612245 + 4.030612245 = 0.000000000 0.000000000 + x = -4.105859224 + 4.030612245 x = -4.105859224 + 4.030612245 Combine like terms: -4.105859224 + 4.030612245 = -0.075246979 x = -0.075246979 Simplifying x = -0.075246979Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.136471469, -0.075246979}
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