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Simplifying 7x2 + 280x + 160 = 0 Reorder the terms: 160 + 280x + 7x2 = 0 Solving 160 + 280x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 22.85714286 + 40x + x2 = 0 Move the constant term to the right: Add '-22.85714286' to each side of the equation. 22.85714286 + 40x + -22.85714286 + x2 = 0 + -22.85714286 Reorder the terms: 22.85714286 + -22.85714286 + 40x + x2 = 0 + -22.85714286 Combine like terms: 22.85714286 + -22.85714286 = 0.00000000 0.00000000 + 40x + x2 = 0 + -22.85714286 40x + x2 = 0 + -22.85714286 Combine like terms: 0 + -22.85714286 = -22.85714286 40x + x2 = -22.85714286 The x term is 40x. Take half its coefficient (20). Square it (400) and add it to both sides. Add '400' to each side of the equation. 40x + 400 + x2 = -22.85714286 + 400 Reorder the terms: 400 + 40x + x2 = -22.85714286 + 400 Combine like terms: -22.85714286 + 400 = 377.14285714 400 + 40x + x2 = 377.14285714 Factor a perfect square on the left side: (x + 20)(x + 20) = 377.14285714 Calculate the square root of the right side: 19.420166249 Break this problem into two subproblems by setting (x + 20) equal to 19.420166249 and -19.420166249.Subproblem 1
x + 20 = 19.420166249 Simplifying x + 20 = 19.420166249 Reorder the terms: 20 + x = 19.420166249 Solving 20 + x = 19.420166249 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x = 19.420166249 + -20 Combine like terms: 20 + -20 = 0 0 + x = 19.420166249 + -20 x = 19.420166249 + -20 Combine like terms: 19.420166249 + -20 = -0.579833751 x = -0.579833751 Simplifying x = -0.579833751Subproblem 2
x + 20 = -19.420166249 Simplifying x + 20 = -19.420166249 Reorder the terms: 20 + x = -19.420166249 Solving 20 + x = -19.420166249 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x = -19.420166249 + -20 Combine like terms: 20 + -20 = 0 0 + x = -19.420166249 + -20 x = -19.420166249 + -20 Combine like terms: -19.420166249 + -20 = -39.420166249 x = -39.420166249 Simplifying x = -39.420166249Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.579833751, -39.420166249}
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