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Simplifying 73x(5x + -19) = 180 Reorder the terms: 73x(-19 + 5x) = 180 (-19 * 73x + 5x * 73x) = 180 (-1387x + 365x2) = 180 Solving -1387x + 365x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + -1387x + 365x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + -1387x + 365x2 = 0 Begin completing the square. Divide all terms by 365 the coefficient of the squared term: Divide each side by '365'. -0.4931506849 + -3.8x + x2 = 0 Move the constant term to the right: Add '0.4931506849' to each side of the equation. -0.4931506849 + -3.8x + 0.4931506849 + x2 = 0 + 0.4931506849 Reorder the terms: -0.4931506849 + 0.4931506849 + -3.8x + x2 = 0 + 0.4931506849 Combine like terms: -0.4931506849 + 0.4931506849 = 0.0000000000 0.0000000000 + -3.8x + x2 = 0 + 0.4931506849 -3.8x + x2 = 0 + 0.4931506849 Combine like terms: 0 + 0.4931506849 = 0.4931506849 -3.8x + x2 = 0.4931506849 The x term is -3.8x. Take half its coefficient (-1.9). Square it (3.61) and add it to both sides. Add '3.61' to each side of the equation. -3.8x + 3.61 + x2 = 0.4931506849 + 3.61 Reorder the terms: 3.61 + -3.8x + x2 = 0.4931506849 + 3.61 Combine like terms: 0.4931506849 + 3.61 = 4.1031506849 3.61 + -3.8x + x2 = 4.1031506849 Factor a perfect square on the left side: (x + -1.9)(x + -1.9) = 4.1031506849 Calculate the square root of the right side: 2.02562353 Break this problem into two subproblems by setting (x + -1.9) equal to 2.02562353 and -2.02562353.Subproblem 1
x + -1.9 = 2.02562353 Simplifying x + -1.9 = 2.02562353 Reorder the terms: -1.9 + x = 2.02562353 Solving -1.9 + x = 2.02562353 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.9' to each side of the equation. -1.9 + 1.9 + x = 2.02562353 + 1.9 Combine like terms: -1.9 + 1.9 = 0.0 0.0 + x = 2.02562353 + 1.9 x = 2.02562353 + 1.9 Combine like terms: 2.02562353 + 1.9 = 3.92562353 x = 3.92562353 Simplifying x = 3.92562353Subproblem 2
x + -1.9 = -2.02562353 Simplifying x + -1.9 = -2.02562353 Reorder the terms: -1.9 + x = -2.02562353 Solving -1.9 + x = -2.02562353 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.9' to each side of the equation. -1.9 + 1.9 + x = -2.02562353 + 1.9 Combine like terms: -1.9 + 1.9 = 0.0 0.0 + x = -2.02562353 + 1.9 x = -2.02562353 + 1.9 Combine like terms: -2.02562353 + 1.9 = -0.12562353 x = -0.12562353 Simplifying x = -0.12562353Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.92562353, -0.12562353}
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