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Simplifying 1 + -0.4x + -0.5x2 = 0 Solving 1 + -0.4x + -0.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. -2 + 0.8x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 0.8x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 0.8x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 0.8x + x2 = 0 + 2 0.8x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 0.8x + x2 = 2 The x term is 0.8x. Take half its coefficient (0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. 0.8x + 0.16 + x2 = 2 + 0.16 Reorder the terms: 0.16 + 0.8x + x2 = 2 + 0.16 Combine like terms: 2 + 0.16 = 2.16 0.16 + 0.8x + x2 = 2.16 Factor a perfect square on the left side: (x + 0.4)(x + 0.4) = 2.16 Calculate the square root of the right side: 1.469693846 Break this problem into two subproblems by setting (x + 0.4) equal to 1.469693846 and -1.469693846.Subproblem 1
x + 0.4 = 1.469693846 Simplifying x + 0.4 = 1.469693846 Reorder the terms: 0.4 + x = 1.469693846 Solving 0.4 + x = 1.469693846 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = 1.469693846 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = 1.469693846 + -0.4 x = 1.469693846 + -0.4 Combine like terms: 1.469693846 + -0.4 = 1.069693846 x = 1.069693846 Simplifying x = 1.069693846Subproblem 2
x + 0.4 = -1.469693846 Simplifying x + 0.4 = -1.469693846 Reorder the terms: 0.4 + x = -1.469693846 Solving 0.4 + x = -1.469693846 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = -1.469693846 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = -1.469693846 + -0.4 x = -1.469693846 + -0.4 Combine like terms: -1.469693846 + -0.4 = -1.869693846 x = -1.869693846 Simplifying x = -1.869693846Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.069693846, -1.869693846}
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