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Simplifying 40 = 0.4x + 0.2x2 Solving 40 = 0.4x + 0.2x2 Solving for variable 'x'. Reorder the terms: 40 + -0.4x + -0.2x2 = 0.4x + -0.4x + 0.2x2 + -0.2x2 Combine like terms: 0.4x + -0.4x = 0.0 40 + -0.4x + -0.2x2 = 0.0 + 0.2x2 + -0.2x2 40 + -0.4x + -0.2x2 = 0.2x2 + -0.2x2 Combine like terms: 0.2x2 + -0.2x2 = 0.0 40 + -0.4x + -0.2x2 = 0.0 Begin completing the square. Divide all terms by -0.2 the coefficient of the squared term: Divide each side by '-0.2'. -200 + 2x + x2 = 0 Move the constant term to the right: Add '200' to each side of the equation. -200 + 2x + 200 + x2 = 0 + 200 Reorder the terms: -200 + 200 + 2x + x2 = 0 + 200 Combine like terms: -200 + 200 = 0 0 + 2x + x2 = 0 + 200 2x + x2 = 0 + 200 Combine like terms: 0 + 200 = 200 2x + x2 = 200 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 200 + 1 Reorder the terms: 1 + 2x + x2 = 200 + 1 Combine like terms: 200 + 1 = 201 1 + 2x + x2 = 201 Factor a perfect square on the left side: (x + 1)(x + 1) = 201 Calculate the square root of the right side: 14.177446879 Break this problem into two subproblems by setting (x + 1) equal to 14.177446879 and -14.177446879.Subproblem 1
x + 1 = 14.177446879 Simplifying x + 1 = 14.177446879 Reorder the terms: 1 + x = 14.177446879 Solving 1 + x = 14.177446879 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 14.177446879 + -1 Combine like terms: 1 + -1 = 0 0 + x = 14.177446879 + -1 x = 14.177446879 + -1 Combine like terms: 14.177446879 + -1 = 13.177446879 x = 13.177446879 Simplifying x = 13.177446879Subproblem 2
x + 1 = -14.177446879 Simplifying x + 1 = -14.177446879 Reorder the terms: 1 + x = -14.177446879 Solving 1 + x = -14.177446879 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -14.177446879 + -1 Combine like terms: 1 + -1 = 0 0 + x = -14.177446879 + -1 x = -14.177446879 + -1 Combine like terms: -14.177446879 + -1 = -15.177446879 x = -15.177446879 Simplifying x = -15.177446879Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.177446879, -15.177446879}
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