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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 = 21.212238211 x = 21.212238211 Simplifying x = 21.212238211Subproblem 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 = -1.212238211 x = -1.212238211 Simplifying x = -1.212238211Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.212238211, -1.212238211}
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