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Simplifying 15 + 3.5x + -4.9x2 = 0 Solving 15 + 3.5x + -4.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -3.06122449 + -0.7142857143x + x2 = 0 Move the constant term to the right: Add '3.06122449' to each side of the equation. -3.06122449 + -0.7142857143x + 3.06122449 + x2 = 0 + 3.06122449 Reorder the terms: -3.06122449 + 3.06122449 + -0.7142857143x + x2 = 0 + 3.06122449 Combine like terms: -3.06122449 + 3.06122449 = 0.00000000 0.00000000 + -0.7142857143x + x2 = 0 + 3.06122449 -0.7142857143x + x2 = 0 + 3.06122449 Combine like terms: 0 + 3.06122449 = 3.06122449 -0.7142857143x + x2 = 3.06122449 The x term is -0.7142857143x. Take half its coefficient (-0.3571428572). Square it (0.1275510204) and add it to both sides. Add '0.1275510204' to each side of the equation. -0.7142857143x + 0.1275510204 + x2 = 3.06122449 + 0.1275510204 Reorder the terms: 0.1275510204 + -0.7142857143x + x2 = 3.06122449 + 0.1275510204 Combine like terms: 3.06122449 + 0.1275510204 = 3.1887755104 0.1275510204 + -0.7142857143x + x2 = 3.1887755104 Factor a perfect square on the left side: (x + -0.3571428572)(x + -0.3571428572) = 3.1887755104 Calculate the square root of the right side: 1.785714286 Break this problem into two subproblems by setting (x + -0.3571428572) equal to 1.785714286 and -1.785714286.Subproblem 1
x + -0.3571428572 = 1.785714286 Simplifying x + -0.3571428572 = 1.785714286 Reorder the terms: -0.3571428572 + x = 1.785714286 Solving -0.3571428572 + x = 1.785714286 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3571428572' to each side of the equation. -0.3571428572 + 0.3571428572 + x = 1.785714286 + 0.3571428572 Combine like terms: -0.3571428572 + 0.3571428572 = 0.0000000000 0.0000000000 + x = 1.785714286 + 0.3571428572 x = 1.785714286 + 0.3571428572 Combine like terms: 1.785714286 + 0.3571428572 = 2.1428571432 x = 2.1428571432 Simplifying x = 2.1428571432Subproblem 2
x + -0.3571428572 = -1.785714286 Simplifying x + -0.3571428572 = -1.785714286 Reorder the terms: -0.3571428572 + x = -1.785714286 Solving -0.3571428572 + x = -1.785714286 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3571428572' to each side of the equation. -0.3571428572 + 0.3571428572 + x = -1.785714286 + 0.3571428572 Combine like terms: -0.3571428572 + 0.3571428572 = 0.0000000000 0.0000000000 + x = -1.785714286 + 0.3571428572 x = -1.785714286 + 0.3571428572 Combine like terms: -1.785714286 + 0.3571428572 = -1.4285714288 x = -1.4285714288 Simplifying x = -1.4285714288Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.1428571432, -1.4285714288}
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