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Simplifying 4.9x2 + -17.5x + 10 = 0 Reorder the terms: 10 + -17.5x + 4.9x2 = 0 Solving 10 + -17.5x + 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 + -3.571428571x + x2 = 0 Move the constant term to the right: Add '-2.040816327' to each side of the equation. 2.040816327 + -3.571428571x + -2.040816327 + x2 = 0 + -2.040816327 Reorder the terms: 2.040816327 + -2.040816327 + -3.571428571x + x2 = 0 + -2.040816327 Combine like terms: 2.040816327 + -2.040816327 = 0.000000000 0.000000000 + -3.571428571x + x2 = 0 + -2.040816327 -3.571428571x + x2 = 0 + -2.040816327 Combine like terms: 0 + -2.040816327 = -2.040816327 -3.571428571x + x2 = -2.040816327 The x term is -3.571428571x. Take half its coefficient (-1.785714286). Square it (3.188775511) and add it to both sides. Add '3.188775511' to each side of the equation. -3.571428571x + 3.188775511 + x2 = -2.040816327 + 3.188775511 Reorder the terms: 3.188775511 + -3.571428571x + x2 = -2.040816327 + 3.188775511 Combine like terms: -2.040816327 + 3.188775511 = 1.147959184 3.188775511 + -3.571428571x + x2 = 1.147959184 Factor a perfect square on the left side: (x + -1.785714286)(x + -1.785714286) = 1.147959184 Calculate the square root of the right side: 1.071428572 Break this problem into two subproblems by setting (x + -1.785714286) equal to 1.071428572 and -1.071428572.Subproblem 1
x + -1.785714286 = 1.071428572 Simplifying x + -1.785714286 = 1.071428572 Reorder the terms: -1.785714286 + x = 1.071428572 Solving -1.785714286 + x = 1.071428572 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.785714286' to each side of the equation. -1.785714286 + 1.785714286 + x = 1.071428572 + 1.785714286 Combine like terms: -1.785714286 + 1.785714286 = 0.000000000 0.000000000 + x = 1.071428572 + 1.785714286 x = 1.071428572 + 1.785714286 Combine like terms: 1.071428572 + 1.785714286 = 2.857142858 x = 2.857142858 Simplifying x = 2.857142858Subproblem 2
x + -1.785714286 = -1.071428572 Simplifying x + -1.785714286 = -1.071428572 Reorder the terms: -1.785714286 + x = -1.071428572 Solving -1.785714286 + x = -1.071428572 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.785714286' to each side of the equation. -1.785714286 + 1.785714286 + x = -1.071428572 + 1.785714286 Combine like terms: -1.785714286 + 1.785714286 = 0.000000000 0.000000000 + x = -1.071428572 + 1.785714286 x = -1.071428572 + 1.785714286 Combine like terms: -1.071428572 + 1.785714286 = 0.714285714 x = 0.714285714 Simplifying x = 0.714285714Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.857142858, 0.714285714}
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