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Simplifying 7x(x + 20) = 20 Reorder the terms: 7x(20 + x) = 20 (20 * 7x + x * 7x) = 20 (140x + 7x2) = 20 Solving 140x + 7x2 = 20 Solving for variable 'x'. Reorder the terms: -20 + 140x + 7x2 = 20 + -20 Combine like terms: 20 + -20 = 0 -20 + 140x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -2.857142857 + 20x + x2 = 0 Move the constant term to the right: Add '2.857142857' to each side of the equation. -2.857142857 + 20x + 2.857142857 + x2 = 0 + 2.857142857 Reorder the terms: -2.857142857 + 2.857142857 + 20x + x2 = 0 + 2.857142857 Combine like terms: -2.857142857 + 2.857142857 = 0.000000000 0.000000000 + 20x + x2 = 0 + 2.857142857 20x + x2 = 0 + 2.857142857 Combine like terms: 0 + 2.857142857 = 2.857142857 20x + x2 = 2.857142857 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = 2.857142857 + 100 Reorder the terms: 100 + 20x + x2 = 2.857142857 + 100 Combine like terms: 2.857142857 + 100 = 102.857142857 100 + 20x + x2 = 102.857142857 Factor a perfect square on the left side: (x + 10)(x + 10) = 102.857142857 Calculate the square root of the right side: 10.141851057 Break this problem into two subproblems by setting (x + 10) equal to 10.141851057 and -10.141851057.Subproblem 1
x + 10 = 10.141851057 Simplifying x + 10 = 10.141851057 Reorder the terms: 10 + x = 10.141851057 Solving 10 + x = 10.141851057 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 10.141851057 + -10 Combine like terms: 10 + -10 = 0 0 + x = 10.141851057 + -10 x = 10.141851057 + -10 Combine like terms: 10.141851057 + -10 = 0.141851057 x = 0.141851057 Simplifying x = 0.141851057Subproblem 2
x + 10 = -10.141851057 Simplifying x + 10 = -10.141851057 Reorder the terms: 10 + x = -10.141851057 Solving 10 + x = -10.141851057 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -10.141851057 + -10 Combine like terms: 10 + -10 = 0 0 + x = -10.141851057 + -10 x = -10.141851057 + -10 Combine like terms: -10.141851057 + -10 = -20.141851057 x = -20.141851057 Simplifying x = -20.141851057Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.141851057, -20.141851057}
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