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Simplifying x2 + 1.6x + 0.64 = 0 Reorder the terms: 0.64 + 1.6x + x2 = 0 Solving 0.64 + 1.6x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.64' to each side of the equation. 0.64 + 1.6x + -0.64 + x2 = 0 + -0.64 Reorder the terms: 0.64 + -0.64 + 1.6x + x2 = 0 + -0.64 Combine like terms: 0.64 + -0.64 = 0.00 0.00 + 1.6x + x2 = 0 + -0.64 1.6x + x2 = 0 + -0.64 Combine like terms: 0 + -0.64 = -0.64 1.6x + x2 = -0.64 The x term is 1.6x. Take half its coefficient (0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. 1.6x + 0.64 + x2 = -0.64 + 0.64 Reorder the terms: 0.64 + 1.6x + x2 = -0.64 + 0.64 Combine like terms: -0.64 + 0.64 = 0.00 0.64 + 1.6x + x2 = 0.00 Factor a perfect square on the left side: (x + 0.8)(x + 0.8) = 0.00 Calculate the square root of the right side: 0.00 Break this problem into two subproblems by setting (x + 0.8) equal to 0.00 and 0.00.Subproblem 1
x + 0.8 = 0.00 Simplifying x + 0.8 = 0.00 Reorder the terms: 0.8 + x = 0.00 Solving 0.8 + x = 0.00 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + x = 0.00 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = 0.00 + -0.8 x = 0.00 + -0.8 Combine like terms: 0.00 + -0.8 = -0.8 x = -0.8 Simplifying x = -0.8Subproblem 2
x + 0.8 = 0.00 Simplifying x + 0.8 = 0.00 Reorder the terms: 0.8 + x = 0.00 Solving 0.8 + x = 0.00 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + x = 0.00 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = 0.00 + -0.8 x = 0.00 + -0.8 Combine like terms: 0.00 + -0.8 = -0.8 x = -0.8 Simplifying x = -0.8Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.8, -0.8}
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