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Simplifying 7x2 + 30x + -160 = 0 Reorder the terms: -160 + 30x + 7x2 = 0 Solving -160 + 30x + 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 + 4.285714286x + x2 = 0 Move the constant term to the right: Add '22.85714286' to each side of the equation. -22.85714286 + 4.285714286x + 22.85714286 + x2 = 0 + 22.85714286 Reorder the terms: -22.85714286 + 22.85714286 + 4.285714286x + x2 = 0 + 22.85714286 Combine like terms: -22.85714286 + 22.85714286 = 0.00000000 0.00000000 + 4.285714286x + x2 = 0 + 22.85714286 4.285714286x + x2 = 0 + 22.85714286 Combine like terms: 0 + 22.85714286 = 22.85714286 4.285714286x + x2 = 22.85714286 The x term is 4.285714286x. Take half its coefficient (2.142857143). Square it (4.591836735) and add it to both sides. Add '4.591836735' to each side of the equation. 4.285714286x + 4.591836735 + x2 = 22.85714286 + 4.591836735 Reorder the terms: 4.591836735 + 4.285714286x + x2 = 22.85714286 + 4.591836735 Combine like terms: 22.85714286 + 4.591836735 = 27.448979595 4.591836735 + 4.285714286x + x2 = 27.448979595 Factor a perfect square on the left side: (x + 2.142857143)(x + 2.142857143) = 27.448979595 Calculate the square root of the right side: 5.239177378 Break this problem into two subproblems by setting (x + 2.142857143) equal to 5.239177378 and -5.239177378.Subproblem 1
x + 2.142857143 = 5.239177378 Simplifying x + 2.142857143 = 5.239177378 Reorder the terms: 2.142857143 + x = 5.239177378 Solving 2.142857143 + x = 5.239177378 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.142857143' to each side of the equation. 2.142857143 + -2.142857143 + x = 5.239177378 + -2.142857143 Combine like terms: 2.142857143 + -2.142857143 = 0.000000000 0.000000000 + x = 5.239177378 + -2.142857143 x = 5.239177378 + -2.142857143 Combine like terms: 5.239177378 + -2.142857143 = 3.096320235 x = 3.096320235 Simplifying x = 3.096320235Subproblem 2
x + 2.142857143 = -5.239177378 Simplifying x + 2.142857143 = -5.239177378 Reorder the terms: 2.142857143 + x = -5.239177378 Solving 2.142857143 + x = -5.239177378 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.142857143' to each side of the equation. 2.142857143 + -2.142857143 + x = -5.239177378 + -2.142857143 Combine like terms: 2.142857143 + -2.142857143 = 0.000000000 0.000000000 + x = -5.239177378 + -2.142857143 x = -5.239177378 + -2.142857143 Combine like terms: -5.239177378 + -2.142857143 = -7.382034521 x = -7.382034521 Simplifying x = -7.382034521Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.096320235, -7.382034521}
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