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Simplifying -0.004x2 + 0.64x + 1.94 = 0 Reorder the terms: 1.94 + 0.64x + -0.004x2 = 0 Solving 1.94 + 0.64x + -0.004x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.004 the coefficient of the squared term: Divide each side by '-0.004'. -485 + -160x + x2 = 0 Move the constant term to the right: Add '485' to each side of the equation. -485 + -160x + 485 + x2 = 0 + 485 Reorder the terms: -485 + 485 + -160x + x2 = 0 + 485 Combine like terms: -485 + 485 = 0 0 + -160x + x2 = 0 + 485 -160x + x2 = 0 + 485 Combine like terms: 0 + 485 = 485 -160x + x2 = 485 The x term is -160x. Take half its coefficient (-80). Square it (6400) and add it to both sides. Add '6400' to each side of the equation. -160x + 6400 + x2 = 485 + 6400 Reorder the terms: 6400 + -160x + x2 = 485 + 6400 Combine like terms: 485 + 6400 = 6885 6400 + -160x + x2 = 6885 Factor a perfect square on the left side: (x + -80)(x + -80) = 6885 Calculate the square root of the right side: 82.975900116 Break this problem into two subproblems by setting (x + -80) equal to 82.975900116 and -82.975900116.Subproblem 1
x + -80 = 82.975900116 Simplifying x + -80 = 82.975900116 Reorder the terms: -80 + x = 82.975900116 Solving -80 + x = 82.975900116 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '80' to each side of the equation. -80 + 80 + x = 82.975900116 + 80 Combine like terms: -80 + 80 = 0 0 + x = 82.975900116 + 80 x = 82.975900116 + 80 Combine like terms: 82.975900116 + 80 = 162.975900116 x = 162.975900116 Simplifying x = 162.975900116Subproblem 2
x + -80 = -82.975900116 Simplifying x + -80 = -82.975900116 Reorder the terms: -80 + x = -82.975900116 Solving -80 + x = -82.975900116 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '80' to each side of the equation. -80 + 80 + x = -82.975900116 + 80 Combine like terms: -80 + 80 = 0 0 + x = -82.975900116 + 80 x = -82.975900116 + 80 Combine like terms: -82.975900116 + 80 = -2.975900116 x = -2.975900116 Simplifying x = -2.975900116Solution
The solution to the problem is based on the solutions from the subproblems. x = {162.975900116, -2.975900116}
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