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Simplifying -4.9x2 + 3.5x + 10 = 0 Reorder the terms: 10 + 3.5x + -4.9x2 = 0 Solving 10 + 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'. -2.040816327 + -0.7142857143x + x2 = 0 Move the constant term to the right: Add '2.040816327' to each side of the equation. -2.040816327 + -0.7142857143x + 2.040816327 + x2 = 0 + 2.040816327 Reorder the terms: -2.040816327 + 2.040816327 + -0.7142857143x + x2 = 0 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + -0.7142857143x + x2 = 0 + 2.040816327 -0.7142857143x + x2 = 0 + 2.040816327 Combine like terms: 0 + 2.040816327 = 2.040816327 -0.7142857143x + x2 = 2.040816327 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 = 2.040816327 + 0.1275510204 Reorder the terms: 0.1275510204 + -0.7142857143x + x2 = 2.040816327 + 0.1275510204 Combine like terms: 2.040816327 + 0.1275510204 = 2.1683673474 0.1275510204 + -0.7142857143x + x2 = 2.1683673474 Factor a perfect square on the left side: (x + -0.3571428572)(x + -0.3571428572) = 2.1683673474 Calculate the square root of the right side: 1.472537724 Break this problem into two subproblems by setting (x + -0.3571428572) equal to 1.472537724 and -1.472537724.Subproblem 1
x + -0.3571428572 = 1.472537724 Simplifying x + -0.3571428572 = 1.472537724 Reorder the terms: -0.3571428572 + x = 1.472537724 Solving -0.3571428572 + x = 1.472537724 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 = 1.472537724 + 0.3571428572 Combine like terms: -0.3571428572 + 0.3571428572 = 0.0000000000 0.0000000000 + x = 1.472537724 + 0.3571428572 x = 1.472537724 + 0.3571428572 Combine like terms: 1.472537724 + 0.3571428572 = 1.8296805812 x = 1.8296805812 Simplifying x = 1.8296805812Subproblem 2
x + -0.3571428572 = -1.472537724 Simplifying x + -0.3571428572 = -1.472537724 Reorder the terms: -0.3571428572 + x = -1.472537724 Solving -0.3571428572 + x = -1.472537724 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 = -1.472537724 + 0.3571428572 Combine like terms: -0.3571428572 + 0.3571428572 = 0.0000000000 0.0000000000 + x = -1.472537724 + 0.3571428572 x = -1.472537724 + 0.3571428572 Combine like terms: -1.472537724 + 0.3571428572 = -1.1153948668 x = -1.1153948668 Simplifying x = -1.1153948668Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.8296805812, -1.1153948668}
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