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Simplifying x2 + -1.8x + 0.81 = 0 Reorder the terms: 0.81 + -1.8x + x2 = 0 Solving 0.81 + -1.8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.81' to each side of the equation. 0.81 + -1.8x + -0.81 + x2 = 0 + -0.81 Reorder the terms: 0.81 + -0.81 + -1.8x + x2 = 0 + -0.81 Combine like terms: 0.81 + -0.81 = 0.00 0.00 + -1.8x + x2 = 0 + -0.81 -1.8x + x2 = 0 + -0.81 Combine like terms: 0 + -0.81 = -0.81 -1.8x + x2 = -0.81 The x term is -1.8x. Take half its coefficient (-0.9). Square it (0.81) and add it to both sides. Add '0.81' to each side of the equation. -1.8x + 0.81 + x2 = -0.81 + 0.81 Reorder the terms: 0.81 + -1.8x + x2 = -0.81 + 0.81 Combine like terms: -0.81 + 0.81 = 0.00 0.81 + -1.8x + x2 = 0.00 Factor a perfect square on the left side: (x + -0.9)(x + -0.9) = 0.00 Calculate the square root of the right side: 0.00 Break this problem into two subproblems by setting (x + -0.9) equal to 0.00 and 0.00.Subproblem 1
x + -0.9 = 0.00 Simplifying x + -0.9 = 0.00 Reorder the terms: -0.9 + x = 0.00 Solving -0.9 + x = 0.00 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + x = 0.00 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + x = 0.00 + 0.9 x = 0.00 + 0.9 Combine like terms: 0.00 + 0.9 = 0.9 x = 0.9 Simplifying x = 0.9Subproblem 2
x + -0.9 = 0.00 Simplifying x + -0.9 = 0.00 Reorder the terms: -0.9 + x = 0.00 Solving -0.9 + x = 0.00 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + x = 0.00 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + x = 0.00 + 0.9 x = 0.00 + 0.9 Combine like terms: 0.00 + 0.9 = 0.9 x = 0.9 Simplifying x = 0.9Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9, 0.9}
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