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Simplifying 3x2 + 500x + 300 = 0 Reorder the terms: 300 + 500x + 3x2 = 0 Solving 300 + 500x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 100 + 166.6666667x + x2 = 0 Move the constant term to the right: Add '-100' to each side of the equation. 100 + 166.6666667x + -100 + x2 = 0 + -100 Reorder the terms: 100 + -100 + 166.6666667x + x2 = 0 + -100 Combine like terms: 100 + -100 = 0 0 + 166.6666667x + x2 = 0 + -100 166.6666667x + x2 = 0 + -100 Combine like terms: 0 + -100 = -100 166.6666667x + x2 = -100 The x term is 166.6666667x. Take half its coefficient (83.33333335). Square it (6944.444447) and add it to both sides. Add '6944.444447' to each side of the equation. 166.6666667x + 6944.444447 + x2 = -100 + 6944.444447 Reorder the terms: 6944.444447 + 166.6666667x + x2 = -100 + 6944.444447 Combine like terms: -100 + 6944.444447 = 6844.444447 6944.444447 + 166.6666667x + x2 = 6844.444447 Factor a perfect square on the left side: (x + 83.33333335)(x + 83.33333335) = 6844.444447 Calculate the square root of the right side: 82.731157655 Break this problem into two subproblems by setting (x + 83.33333335) equal to 82.731157655 and -82.731157655.Subproblem 1
x + 83.33333335 = 82.731157655 Simplifying x + 83.33333335 = 82.731157655 Reorder the terms: 83.33333335 + x = 82.731157655 Solving 83.33333335 + x = 82.731157655 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-83.33333335' to each side of the equation. 83.33333335 + -83.33333335 + x = 82.731157655 + -83.33333335 Combine like terms: 83.33333335 + -83.33333335 = 0.00000000 0.00000000 + x = 82.731157655 + -83.33333335 x = 82.731157655 + -83.33333335 Combine like terms: 82.731157655 + -83.33333335 = -0.602175695 x = -0.602175695 Simplifying x = -0.602175695Subproblem 2
x + 83.33333335 = -82.731157655 Simplifying x + 83.33333335 = -82.731157655 Reorder the terms: 83.33333335 + x = -82.731157655 Solving 83.33333335 + x = -82.731157655 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-83.33333335' to each side of the equation. 83.33333335 + -83.33333335 + x = -82.731157655 + -83.33333335 Combine like terms: 83.33333335 + -83.33333335 = 0.00000000 0.00000000 + x = -82.731157655 + -83.33333335 x = -82.731157655 + -83.33333335 Combine like terms: -82.731157655 + -83.33333335 = -166.064491005 x = -166.064491005 Simplifying x = -166.064491005Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.602175695, -166.064491005}
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