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Simplifying -0.1x2 + 16x + -50 = 0 Reorder the terms: -50 + 16x + -0.1x2 = 0 Solving -50 + 16x + -0.1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.1 the coefficient of the squared term: Divide each side by '-0.1'. 500 + -160x + x2 = 0 Move the constant term to the right: Add '-500' to each side of the equation. 500 + -160x + -500 + x2 = 0 + -500 Reorder the terms: 500 + -500 + -160x + x2 = 0 + -500 Combine like terms: 500 + -500 = 0 0 + -160x + x2 = 0 + -500 -160x + x2 = 0 + -500 Combine like terms: 0 + -500 = -500 -160x + x2 = -500 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 = -500 + 6400 Reorder the terms: 6400 + -160x + x2 = -500 + 6400 Combine like terms: -500 + 6400 = 5900 6400 + -160x + x2 = 5900 Factor a perfect square on the left side: (x + -80)(x + -80) = 5900 Calculate the square root of the right side: 76.811457479 Break this problem into two subproblems by setting (x + -80) equal to 76.811457479 and -76.811457479.Subproblem 1
x + -80 = 76.811457479 Simplifying x + -80 = 76.811457479 Reorder the terms: -80 + x = 76.811457479 Solving -80 + x = 76.811457479 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 = 76.811457479 + 80 Combine like terms: -80 + 80 = 0 0 + x = 76.811457479 + 80 x = 76.811457479 + 80 Combine like terms: 76.811457479 + 80 = 156.811457479 x = 156.811457479 Simplifying x = 156.811457479Subproblem 2
x + -80 = -76.811457479 Simplifying x + -80 = -76.811457479 Reorder the terms: -80 + x = -76.811457479 Solving -80 + x = -76.811457479 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 = -76.811457479 + 80 Combine like terms: -80 + 80 = 0 0 + x = -76.811457479 + 80 x = -76.811457479 + 80 Combine like terms: -76.811457479 + 80 = 3.188542521 x = 3.188542521 Simplifying x = 3.188542521Solution
The solution to the problem is based on the solutions from the subproblems. x = {156.811457479, 3.188542521}
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