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Simplifying -3.5x2 + -76x + 1444 = 0 Reorder the terms: 1444 + -76x + -3.5x2 = 0 Solving 1444 + -76x + -3.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -3.5 the coefficient of the squared term: Divide each side by '-3.5'. -412.5714286 + 21.71428571x + x2 = 0 Move the constant term to the right: Add '412.5714286' to each side of the equation. -412.5714286 + 21.71428571x + 412.5714286 + x2 = 0 + 412.5714286 Reorder the terms: -412.5714286 + 412.5714286 + 21.71428571x + x2 = 0 + 412.5714286 Combine like terms: -412.5714286 + 412.5714286 = 0.0000000 0.0000000 + 21.71428571x + x2 = 0 + 412.5714286 21.71428571x + x2 = 0 + 412.5714286 Combine like terms: 0 + 412.5714286 = 412.5714286 21.71428571x + x2 = 412.5714286 The x term is 21.71428571x. Take half its coefficient (10.85714286). Square it (117.8775511) and add it to both sides. Add '117.8775511' to each side of the equation. 21.71428571x + 117.8775511 + x2 = 412.5714286 + 117.8775511 Reorder the terms: 117.8775511 + 21.71428571x + x2 = 412.5714286 + 117.8775511 Combine like terms: 412.5714286 + 117.8775511 = 530.4489797 117.8775511 + 21.71428571x + x2 = 530.4489797 Factor a perfect square on the left side: (x + 10.85714286)(x + 10.85714286) = 530.4489797 Calculate the square root of the right side: 23.031478018 Break this problem into two subproblems by setting (x + 10.85714286) equal to 23.031478018 and -23.031478018.Subproblem 1
x + 10.85714286 = 23.031478018 Simplifying x + 10.85714286 = 23.031478018 Reorder the terms: 10.85714286 + x = 23.031478018 Solving 10.85714286 + x = 23.031478018 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.85714286' to each side of the equation. 10.85714286 + -10.85714286 + x = 23.031478018 + -10.85714286 Combine like terms: 10.85714286 + -10.85714286 = 0.00000000 0.00000000 + x = 23.031478018 + -10.85714286 x = 23.031478018 + -10.85714286 Combine like terms: 23.031478018 + -10.85714286 = 12.174335158 x = 12.174335158 Simplifying x = 12.174335158Subproblem 2
x + 10.85714286 = -23.031478018 Simplifying x + 10.85714286 = -23.031478018 Reorder the terms: 10.85714286 + x = -23.031478018 Solving 10.85714286 + x = -23.031478018 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.85714286' to each side of the equation. 10.85714286 + -10.85714286 + x = -23.031478018 + -10.85714286 Combine like terms: 10.85714286 + -10.85714286 = 0.00000000 0.00000000 + x = -23.031478018 + -10.85714286 x = -23.031478018 + -10.85714286 Combine like terms: -23.031478018 + -10.85714286 = -33.888620878 x = -33.888620878 Simplifying x = -33.888620878Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.174335158, -33.888620878}
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