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Simplifying x2 + 1.8x = 0.162 Reorder the terms: 1.8x + x2 = 0.162 Solving 1.8x + x2 = 0.162 Solving for variable 'x'. Reorder the terms: -0.162 + 1.8x + x2 = 0.162 + -0.162 Combine like terms: 0.162 + -0.162 = 0.000 -0.162 + 1.8x + x2 = 0.000 Begin completing the square. Move the constant term to the right: Add '0.162' to each side of the equation. -0.162 + 1.8x + 0.162 + x2 = 0.000 + 0.162 Reorder the terms: -0.162 + 0.162 + 1.8x + x2 = 0.000 + 0.162 Combine like terms: -0.162 + 0.162 = 0.000 0.000 + 1.8x + x2 = 0.000 + 0.162 1.8x + x2 = 0.000 + 0.162 Combine like terms: 0.000 + 0.162 = 0.162 1.8x + x2 = 0.162 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 = 0.162 + 0.81 Reorder the terms: 0.81 + 1.8x + x2 = 0.162 + 0.81 Combine like terms: 0.162 + 0.81 = 0.972 0.81 + 1.8x + x2 = 0.972 Factor a perfect square on the left side: (x + 0.9)(x + 0.9) = 0.972 Calculate the square root of the right side: 0.985900604 Break this problem into two subproblems by setting (x + 0.9) equal to 0.985900604 and -0.985900604.Subproblem 1
x + 0.9 = 0.985900604 Simplifying x + 0.9 = 0.985900604 Reorder the terms: 0.9 + x = 0.985900604 Solving 0.9 + x = 0.985900604 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 = 0.985900604 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = 0.985900604 + -0.9 x = 0.985900604 + -0.9 Combine like terms: 0.985900604 + -0.9 = 0.085900604 x = 0.085900604 Simplifying x = 0.085900604Subproblem 2
x + 0.9 = -0.985900604 Simplifying x + 0.9 = -0.985900604 Reorder the terms: 0.9 + x = -0.985900604 Solving 0.9 + x = -0.985900604 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 = -0.985900604 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = -0.985900604 + -0.9 x = -0.985900604 + -0.9 Combine like terms: -0.985900604 + -0.9 = -1.885900604 x = -1.885900604 Simplifying x = -1.885900604Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.085900604, -1.885900604}
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