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Simplifying (9x2) + -1(180x) + -6400 = 0 Remove parenthesis around (180x) (9x2) + -1 * 180x + -6400 = 0 Multiply -1 * 180 (9x2) + -180x + -6400 = 0 Reorder the terms: -6400 + -180x + (9x2) = 0 Solving -6400 + -180x + (9x2) = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -711.1111111 + -20x + x2 = 0 Move the constant term to the right: Add '711.1111111' to each side of the equation. -711.1111111 + -20x + 711.1111111 + x2 = 0 + 711.1111111 Reorder the terms: -711.1111111 + 711.1111111 + -20x + x2 = 0 + 711.1111111 Combine like terms: -711.1111111 + 711.1111111 = 0.0000000 0.0000000 + -20x + x2 = 0 + 711.1111111 -20x + x2 = 0 + 711.1111111 Combine like terms: 0 + 711.1111111 = 711.1111111 -20x + x2 = 711.1111111 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 = 711.1111111 + 100 Reorder the terms: 100 + -20x + x2 = 711.1111111 + 100 Combine like terms: 711.1111111 + 100 = 811.1111111 100 + -20x + x2 = 811.1111111 Factor a perfect square on the left side: ((x) + -10)((x) + -10) = 811.1111111 Calculate the square root of the right side: 28.480012484 Break this problem into two subproblems by setting ((x) + -10) equal to 28.480012484 and -28.480012484.Subproblem 1
(x) + -10 = 28.480012484 Simplifying (x) + -10 = 28.480012484 x + -10 = 28.480012484 Reorder the terms: -10 + x = 28.480012484 Solving -10 + x = 28.480012484 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 = 28.480012484 + 10 Combine like terms: -10 + 10 = 0 0 + x = 28.480012484 + 10 x = 28.480012484 + 10 Combine like terms: 28.480012484 + 10 = 38.480012484 x = 38.480012484 Simplifying x = 38.480012484Subproblem 2
(x) + -10 = -28.480012484 Simplifying (x) + -10 = -28.480012484 x + -10 = -28.480012484 Reorder the terms: -10 + x = -28.480012484 Solving -10 + x = -28.480012484 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 = -28.480012484 + 10 Combine like terms: -10 + 10 = 0 0 + x = -28.480012484 + 10 x = -28.480012484 + 10 Combine like terms: -28.480012484 + 10 = -18.480012484 x = -18.480012484 Simplifying x = -18.480012484Solution
The solution to the problem is based on the solutions from the subproblems. x = {38.480012484, -18.480012484}
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