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Simplifying 305x + 150x(x + 50) = 34800 Reorder the terms: 305x + 150x(50 + x) = 34800 305x + (50 * 150x + x * 150x) = 34800 305x + (7500x + 150x2) = 34800 Combine like terms: 305x + 7500x = 7805x 7805x + 150x2 = 34800 Solving 7805x + 150x2 = 34800 Solving for variable 'x'. Reorder the terms: -34800 + 7805x + 150x2 = 34800 + -34800 Combine like terms: 34800 + -34800 = 0 -34800 + 7805x + 150x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-6960 + 1561x + 30x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-6960 + 1561x + 30x2)' equal to zero and attempt to solve: Simplifying -6960 + 1561x + 30x2 = 0 Solving -6960 + 1561x + 30x2 = 0 Begin completing the square. Divide all terms by 30 the coefficient of the squared term: Divide each side by '30'. -232 + 52.03333333x + x2 = 0.0 Move the constant term to the right: Add '232' to each side of the equation. -232 + 52.03333333x + 232 + x2 = 0.0 + 232 Reorder the terms: -232 + 232 + 52.03333333x + x2 = 0.0 + 232 Combine like terms: -232 + 232 = 0 0 + 52.03333333x + x2 = 0.0 + 232 52.03333333x + x2 = 0.0 + 232 Combine like terms: 0.0 + 232 = 232 52.03333333x + x2 = 232 The x term is 52.03333333x. Take half its coefficient (26.01666667). Square it (676.8669446) and add it to both sides. Add '676.8669446' to each side of the equation. 52.03333333x + 676.8669446 + x2 = 232 + 676.8669446 Reorder the terms: 676.8669446 + 52.03333333x + x2 = 232 + 676.8669446 Combine like terms: 232 + 676.8669446 = 908.8669446 676.8669446 + 52.03333333x + x2 = 908.8669446 Factor a perfect square on the left side: (x + 26.01666667)(x + 26.01666667) = 908.8669446 Calculate the square root of the right side: 30.147420198 Break this problem into two subproblems by setting (x + 26.01666667) equal to 30.147420198 and -30.147420198.Subproblem 1
x + 26.01666667 = 30.147420198 Simplifying x + 26.01666667 = 30.147420198 Reorder the terms: 26.01666667 + x = 30.147420198 Solving 26.01666667 + x = 30.147420198 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-26.01666667' to each side of the equation. 26.01666667 + -26.01666667 + x = 30.147420198 + -26.01666667 Combine like terms: 26.01666667 + -26.01666667 = 0.00000000 0.00000000 + x = 30.147420198 + -26.01666667 x = 30.147420198 + -26.01666667 Combine like terms: 30.147420198 + -26.01666667 = 4.130753528 x = 4.130753528 Simplifying x = 4.130753528Subproblem 2
x + 26.01666667 = -30.147420198 Simplifying x + 26.01666667 = -30.147420198 Reorder the terms: 26.01666667 + x = -30.147420198 Solving 26.01666667 + x = -30.147420198 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-26.01666667' to each side of the equation. 26.01666667 + -26.01666667 + x = -30.147420198 + -26.01666667 Combine like terms: 26.01666667 + -26.01666667 = 0.00000000 0.00000000 + x = -30.147420198 + -26.01666667 x = -30.147420198 + -26.01666667 Combine like terms: -30.147420198 + -26.01666667 = -56.164086868 x = -56.164086868 Simplifying x = -56.164086868Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.130753528, -56.164086868}Solution
x = {4.130753528, -56.164086868}
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