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Simplifying (-0.4x2 + -0.1x + 1) = 0 Reorder the terms: (1 + -0.1x + -0.4x2) = 0 Remove parenthesis around (1 + -0.1x + -0.4x2) 1 + -0.1x + -0.4x2 = 0 Solving 1 + -0.1x + -0.4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.4 the coefficient of the squared term: Divide each side by '-0.4'. -2.5 + 0.25x + x2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + 0.25x + 2.5 + x2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + 0.25x + x2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + 0.25x + x2 = 0 + 2.5 0.25x + x2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 0.25x + x2 = 2.5 The x term is 0.25x. Take half its coefficient (0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. 0.25x + 0.015625 + x2 = 2.5 + 0.015625 Reorder the terms: 0.015625 + 0.25x + x2 = 2.5 + 0.015625 Combine like terms: 2.5 + 0.015625 = 2.515625 0.015625 + 0.25x + x2 = 2.515625 Factor a perfect square on the left side: (x + 0.125)(x + 0.125) = 2.515625 Calculate the square root of the right side: 1.586072193 Break this problem into two subproblems by setting (x + 0.125) equal to 1.586072193 and -1.586072193.Subproblem 1
x + 0.125 = 1.586072193 Simplifying x + 0.125 = 1.586072193 Reorder the terms: 0.125 + x = 1.586072193 Solving 0.125 + x = 1.586072193 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + x = 1.586072193 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = 1.586072193 + -0.125 x = 1.586072193 + -0.125 Combine like terms: 1.586072193 + -0.125 = 1.461072193 x = 1.461072193 Simplifying x = 1.461072193Subproblem 2
x + 0.125 = -1.586072193 Simplifying x + 0.125 = -1.586072193 Reorder the terms: 0.125 + x = -1.586072193 Solving 0.125 + x = -1.586072193 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + x = -1.586072193 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = -1.586072193 + -0.125 x = -1.586072193 + -0.125 Combine like terms: -1.586072193 + -0.125 = -1.711072193 x = -1.711072193 Simplifying x = -1.711072193Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.461072193, -1.711072193}
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