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Simplifying x2 + -0.4x + -0.77 = 0 Reorder the terms: -0.77 + -0.4x + x2 = 0 Solving -0.77 + -0.4x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.77' to each side of the equation. -0.77 + -0.4x + 0.77 + x2 = 0 + 0.77 Reorder the terms: -0.77 + 0.77 + -0.4x + x2 = 0 + 0.77 Combine like terms: -0.77 + 0.77 = 0.00 0.00 + -0.4x + x2 = 0 + 0.77 -0.4x + x2 = 0 + 0.77 Combine like terms: 0 + 0.77 = 0.77 -0.4x + x2 = 0.77 The x term is -0.4x. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4x + 0.04 + x2 = 0.77 + 0.04 Reorder the terms: 0.04 + -0.4x + x2 = 0.77 + 0.04 Combine like terms: 0.77 + 0.04 = 0.81 0.04 + -0.4x + x2 = 0.81 Factor a perfect square on the left side: (x + -0.2)(x + -0.2) = 0.81 Calculate the square root of the right side: 0.9 Break this problem into two subproblems by setting (x + -0.2) equal to 0.9 and -0.9.Subproblem 1
x + -0.2 = 0.9 Simplifying x + -0.2 = 0.9 Reorder the terms: -0.2 + x = 0.9 Solving -0.2 + x = 0.9 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = 0.9 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = 0.9 + 0.2 x = 0.9 + 0.2 Combine like terms: 0.9 + 0.2 = 1.1 x = 1.1 Simplifying x = 1.1Subproblem 2
x + -0.2 = -0.9 Simplifying x + -0.2 = -0.9 Reorder the terms: -0.2 + x = -0.9 Solving -0.2 + x = -0.9 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = -0.9 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = -0.9 + 0.2 x = -0.9 + 0.2 Combine like terms: -0.9 + 0.2 = -0.7 x = -0.7 Simplifying x = -0.7Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1, -0.7}
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