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Simplifying x(7x + 300) = 50000 Reorder the terms: x(300 + 7x) = 50000 (300 * x + 7x * x) = 50000 (300x + 7x2) = 50000 Solving 300x + 7x2 = 50000 Solving for variable 'x'. Reorder the terms: -50000 + 300x + 7x2 = 50000 + -50000 Combine like terms: 50000 + -50000 = 0 -50000 + 300x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -7142.857143 + 42.85714286x + x2 = 0 Move the constant term to the right: Add '7142.857143' to each side of the equation. -7142.857143 + 42.85714286x + 7142.857143 + x2 = 0 + 7142.857143 Reorder the terms: -7142.857143 + 7142.857143 + 42.85714286x + x2 = 0 + 7142.857143 Combine like terms: -7142.857143 + 7142.857143 = 0.000000 0.000000 + 42.85714286x + x2 = 0 + 7142.857143 42.85714286x + x2 = 0 + 7142.857143 Combine like terms: 0 + 7142.857143 = 7142.857143 42.85714286x + x2 = 7142.857143 The x term is 42.85714286x. Take half its coefficient (21.42857143). Square it (459.1836735) and add it to both sides. Add '459.1836735' to each side of the equation. 42.85714286x + 459.1836735 + x2 = 7142.857143 + 459.1836735 Reorder the terms: 459.1836735 + 42.85714286x + x2 = 7142.857143 + 459.1836735 Combine like terms: 7142.857143 + 459.1836735 = 7602.0408165 459.1836735 + 42.85714286x + x2 = 7602.0408165 Factor a perfect square on the left side: (x + 21.42857143)(x + 21.42857143) = 7602.0408165 Calculate the square root of the right side: 87.189682971 Break this problem into two subproblems by setting (x + 21.42857143) equal to 87.189682971 and -87.189682971.Subproblem 1
x + 21.42857143 = 87.189682971 Simplifying x + 21.42857143 = 87.189682971 Reorder the terms: 21.42857143 + x = 87.189682971 Solving 21.42857143 + x = 87.189682971 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-21.42857143' to each side of the equation. 21.42857143 + -21.42857143 + x = 87.189682971 + -21.42857143 Combine like terms: 21.42857143 + -21.42857143 = 0.00000000 0.00000000 + x = 87.189682971 + -21.42857143 x = 87.189682971 + -21.42857143 Combine like terms: 87.189682971 + -21.42857143 = 65.761111541 x = 65.761111541 Simplifying x = 65.761111541Subproblem 2
x + 21.42857143 = -87.189682971 Simplifying x + 21.42857143 = -87.189682971 Reorder the terms: 21.42857143 + x = -87.189682971 Solving 21.42857143 + x = -87.189682971 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-21.42857143' to each side of the equation. 21.42857143 + -21.42857143 + x = -87.189682971 + -21.42857143 Combine like terms: 21.42857143 + -21.42857143 = 0.00000000 0.00000000 + x = -87.189682971 + -21.42857143 x = -87.189682971 + -21.42857143 Combine like terms: -87.189682971 + -21.42857143 = -108.618254401 x = -108.618254401 Simplifying x = -108.618254401Solution
The solution to the problem is based on the solutions from the subproblems. x = {65.761111541, -108.618254401}
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