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Simplifying 32x + 0.2x2 + -5 = 0 Reorder the terms: -5 + 32x + 0.2x2 = 0 Solving -5 + 32x + 0.2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.2 the coefficient of the squared term: Divide each side by '0.2'. -25 + 160x + x2 = 0 Move the constant term to the right: Add '25' to each side of the equation. -25 + 160x + 25 + x2 = 0 + 25 Reorder the terms: -25 + 25 + 160x + x2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 160x + x2 = 0 + 25 160x + x2 = 0 + 25 Combine like terms: 0 + 25 = 25 160x + x2 = 25 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 = 25 + 6400 Reorder the terms: 6400 + 160x + x2 = 25 + 6400 Combine like terms: 25 + 6400 = 6425 6400 + 160x + x2 = 6425 Factor a perfect square on the left side: (x + 80)(x + 80) = 6425 Calculate the square root of the right side: 80.156097709 Break this problem into two subproblems by setting (x + 80) equal to 80.156097709 and -80.156097709.Subproblem 1
x + 80 = 80.156097709 Simplifying x + 80 = 80.156097709 Reorder the terms: 80 + x = 80.156097709 Solving 80 + x = 80.156097709 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 = 80.156097709 + -80 Combine like terms: 80 + -80 = 0 0 + x = 80.156097709 + -80 x = 80.156097709 + -80 Combine like terms: 80.156097709 + -80 = 0.156097709 x = 0.156097709 Simplifying x = 0.156097709Subproblem 2
x + 80 = -80.156097709 Simplifying x + 80 = -80.156097709 Reorder the terms: 80 + x = -80.156097709 Solving 80 + x = -80.156097709 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 = -80.156097709 + -80 Combine like terms: 80 + -80 = 0 0 + x = -80.156097709 + -80 x = -80.156097709 + -80 Combine like terms: -80.156097709 + -80 = -160.156097709 x = -160.156097709 Simplifying x = -160.156097709Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.156097709, -160.156097709}
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