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Simplifying 180 = 7x(x + 20) Reorder the terms: 180 = 7x(20 + x) 180 = (20 * 7x + x * 7x) 180 = (140x + 7x2) Solving 180 = 140x + 7x2 Solving for variable 'x'. Reorder the terms: 180 + -140x + -7x2 = 140x + -140x + 7x2 + -7x2 Combine like terms: 140x + -140x = 0 180 + -140x + -7x2 = 0 + 7x2 + -7x2 180 + -140x + -7x2 = 7x2 + -7x2 Combine like terms: 7x2 + -7x2 = 0 180 + -140x + -7x2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -25.71428571 + 20x + x2 = 0 Move the constant term to the right: Add '25.71428571' to each side of the equation. -25.71428571 + 20x + 25.71428571 + x2 = 0 + 25.71428571 Reorder the terms: -25.71428571 + 25.71428571 + 20x + x2 = 0 + 25.71428571 Combine like terms: -25.71428571 + 25.71428571 = 0.00000000 0.00000000 + 20x + x2 = 0 + 25.71428571 20x + x2 = 0 + 25.71428571 Combine like terms: 0 + 25.71428571 = 25.71428571 20x + x2 = 25.71428571 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 = 25.71428571 + 100 Reorder the terms: 100 + 20x + x2 = 25.71428571 + 100 Combine like terms: 25.71428571 + 100 = 125.71428571 100 + 20x + x2 = 125.71428571 Factor a perfect square on the left side: (x + 10)(x + 10) = 125.71428571 Calculate the square root of the right side: 11.212238211 Break this problem into two subproblems by setting (x + 10) equal to 11.212238211 and -11.212238211.Subproblem 1
x + 10 = 11.212238211 Simplifying x + 10 = 11.212238211 Reorder the terms: 10 + x = 11.212238211 Solving 10 + x = 11.212238211 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 = 11.212238211 + -10 Combine like terms: 10 + -10 = 0 0 + x = 11.212238211 + -10 x = 11.212238211 + -10 Combine like terms: 11.212238211 + -10 = 1.212238211 x = 1.212238211 Simplifying x = 1.212238211Subproblem 2
x + 10 = -11.212238211 Simplifying x + 10 = -11.212238211 Reorder the terms: 10 + x = -11.212238211 Solving 10 + x = -11.212238211 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 = -11.212238211 + -10 Combine like terms: 10 + -10 = 0 0 + x = -11.212238211 + -10 x = -11.212238211 + -10 Combine like terms: -11.212238211 + -10 = -21.212238211 x = -21.212238211 Simplifying x = -21.212238211Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.212238211, -21.212238211}
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