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Simplifying 0.56x2 + -40x + -400 = 0 Reorder the terms: -400 + -40x + 0.56x2 = 0 Solving -400 + -40x + 0.56x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.56 the coefficient of the squared term: Divide each side by '0.56'. -714.2857143 + -71.42857143x + x2 = 0 Move the constant term to the right: Add '714.2857143' to each side of the equation. -714.2857143 + -71.42857143x + 714.2857143 + x2 = 0 + 714.2857143 Reorder the terms: -714.2857143 + 714.2857143 + -71.42857143x + x2 = 0 + 714.2857143 Combine like terms: -714.2857143 + 714.2857143 = 0.0000000 0.0000000 + -71.42857143x + x2 = 0 + 714.2857143 -71.42857143x + x2 = 0 + 714.2857143 Combine like terms: 0 + 714.2857143 = 714.2857143 -71.42857143x + x2 = 714.2857143 The x term is -71.42857143x. Take half its coefficient (-35.71428572). Square it (1275.510204) and add it to both sides. Add '1275.510204' to each side of the equation. -71.42857143x + 1275.510204 + x2 = 714.2857143 + 1275.510204 Reorder the terms: 1275.510204 + -71.42857143x + x2 = 714.2857143 + 1275.510204 Combine like terms: 714.2857143 + 1275.510204 = 1989.7959183 1275.510204 + -71.42857143x + x2 = 1989.7959183 Factor a perfect square on the left side: (x + -35.71428572)(x + -35.71428572) = 1989.7959183 Calculate the square root of the right side: 44.607128559 Break this problem into two subproblems by setting (x + -35.71428572) equal to 44.607128559 and -44.607128559.Subproblem 1
x + -35.71428572 = 44.607128559 Simplifying x + -35.71428572 = 44.607128559 Reorder the terms: -35.71428572 + x = 44.607128559 Solving -35.71428572 + x = 44.607128559 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '35.71428572' to each side of the equation. -35.71428572 + 35.71428572 + x = 44.607128559 + 35.71428572 Combine like terms: -35.71428572 + 35.71428572 = 0.00000000 0.00000000 + x = 44.607128559 + 35.71428572 x = 44.607128559 + 35.71428572 Combine like terms: 44.607128559 + 35.71428572 = 80.321414279 x = 80.321414279 Simplifying x = 80.321414279Subproblem 2
x + -35.71428572 = -44.607128559 Simplifying x + -35.71428572 = -44.607128559 Reorder the terms: -35.71428572 + x = -44.607128559 Solving -35.71428572 + x = -44.607128559 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '35.71428572' to each side of the equation. -35.71428572 + 35.71428572 + x = -44.607128559 + 35.71428572 Combine like terms: -35.71428572 + 35.71428572 = 0.00000000 0.00000000 + x = -44.607128559 + 35.71428572 x = -44.607128559 + 35.71428572 Combine like terms: -44.607128559 + 35.71428572 = -8.892842839 x = -8.892842839 Simplifying x = -8.892842839Solution
The solution to the problem is based on the solutions from the subproblems. x = {80.321414279, -8.892842839}
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