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Simplifying 0.005x2 + 0.19x + -32 = 0 Reorder the terms: -32 + 0.19x + 0.005x2 = 0 Solving -32 + 0.19x + 0.005x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.005 the coefficient of the squared term: Divide each side by '0.005'. -6400 + 38x + x2 = 0 Move the constant term to the right: Add '6400' to each side of the equation. -6400 + 38x + 6400 + x2 = 0 + 6400 Reorder the terms: -6400 + 6400 + 38x + x2 = 0 + 6400 Combine like terms: -6400 + 6400 = 0 0 + 38x + x2 = 0 + 6400 38x + x2 = 0 + 6400 Combine like terms: 0 + 6400 = 6400 38x + x2 = 6400 The x term is 38x. Take half its coefficient (19). Square it (361) and add it to both sides. Add '361' to each side of the equation. 38x + 361 + x2 = 6400 + 361 Reorder the terms: 361 + 38x + x2 = 6400 + 361 Combine like terms: 6400 + 361 = 6761 361 + 38x + x2 = 6761 Factor a perfect square on the left side: (x + 19)(x + 19) = 6761 Calculate the square root of the right side: 82.225300243 Break this problem into two subproblems by setting (x + 19) equal to 82.225300243 and -82.225300243.Subproblem 1
x + 19 = 82.225300243 Simplifying x + 19 = 82.225300243 Reorder the terms: 19 + x = 82.225300243 Solving 19 + x = 82.225300243 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-19' to each side of the equation. 19 + -19 + x = 82.225300243 + -19 Combine like terms: 19 + -19 = 0 0 + x = 82.225300243 + -19 x = 82.225300243 + -19 Combine like terms: 82.225300243 + -19 = 63.225300243 x = 63.225300243 Simplifying x = 63.225300243Subproblem 2
x + 19 = -82.225300243 Simplifying x + 19 = -82.225300243 Reorder the terms: 19 + x = -82.225300243 Solving 19 + x = -82.225300243 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-19' to each side of the equation. 19 + -19 + x = -82.225300243 + -19 Combine like terms: 19 + -19 = 0 0 + x = -82.225300243 + -19 x = -82.225300243 + -19 Combine like terms: -82.225300243 + -19 = -101.225300243 x = -101.225300243 Simplifying x = -101.225300243Solution
The solution to the problem is based on the solutions from the subproblems. x = {63.225300243, -101.225300243}
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