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Simplifying x2 + 0.09x + -0.9 = 0 Reorder the terms: -0.9 + 0.09x + x2 = 0 Solving -0.9 + 0.09x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.9' to each side of the equation. -0.9 + 0.09x + 0.9 + x2 = 0 + 0.9 Reorder the terms: -0.9 + 0.9 + 0.09x + x2 = 0 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + 0.09x + x2 = 0 + 0.9 0.09x + x2 = 0 + 0.9 Combine like terms: 0 + 0.9 = 0.9 0.09x + x2 = 0.9 The x term is 0.09x. Take half its coefficient (0.045). Square it (0.002025) and add it to both sides. Add '0.002025' to each side of the equation. 0.09x + 0.002025 + x2 = 0.9 + 0.002025 Reorder the terms: 0.002025 + 0.09x + x2 = 0.9 + 0.002025 Combine like terms: 0.9 + 0.002025 = 0.902025 0.002025 + 0.09x + x2 = 0.902025 Factor a perfect square on the left side: (x + 0.045)(x + 0.045) = 0.902025 Calculate the square root of the right side: 0.949749967 Break this problem into two subproblems by setting (x + 0.045) equal to 0.949749967 and -0.949749967.Subproblem 1
x + 0.045 = 0.949749967 Simplifying x + 0.045 = 0.949749967 Reorder the terms: 0.045 + x = 0.949749967 Solving 0.045 + x = 0.949749967 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.045' to each side of the equation. 0.045 + -0.045 + x = 0.949749967 + -0.045 Combine like terms: 0.045 + -0.045 = 0.000 0.000 + x = 0.949749967 + -0.045 x = 0.949749967 + -0.045 Combine like terms: 0.949749967 + -0.045 = 0.904749967 x = 0.904749967 Simplifying x = 0.904749967Subproblem 2
x + 0.045 = -0.949749967 Simplifying x + 0.045 = -0.949749967 Reorder the terms: 0.045 + x = -0.949749967 Solving 0.045 + x = -0.949749967 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.045' to each side of the equation. 0.045 + -0.045 + x = -0.949749967 + -0.045 Combine like terms: 0.045 + -0.045 = 0.000 0.000 + x = -0.949749967 + -0.045 x = -0.949749967 + -0.045 Combine like terms: -0.949749967 + -0.045 = -0.994749967 x = -0.994749967 Simplifying x = -0.994749967Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.904749967, -0.994749967}
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