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Simplifying x2 + -3x + -0.9 = 0 Reorder the terms: -0.9 + -3x + x2 = 0 Solving -0.9 + -3x + 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 + -3x + 0.9 + x2 = 0 + 0.9 Reorder the terms: -0.9 + 0.9 + -3x + x2 = 0 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + -3x + x2 = 0 + 0.9 -3x + x2 = 0 + 0.9 Combine like terms: 0 + 0.9 = 0.9 -3x + x2 = 0.9 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 0.9 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 0.9 + 2.25 Combine like terms: 0.9 + 2.25 = 3.15 2.25 + -3x + x2 = 3.15 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 3.15 Calculate the square root of the right side: 1.774823935 Break this problem into two subproblems by setting (x + -1.5) equal to 1.774823935 and -1.774823935.Subproblem 1
x + -1.5 = 1.774823935 Simplifying x + -1.5 = 1.774823935 Reorder the terms: -1.5 + x = 1.774823935 Solving -1.5 + x = 1.774823935 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 1.774823935 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 1.774823935 + 1.5 x = 1.774823935 + 1.5 Combine like terms: 1.774823935 + 1.5 = 3.274823935 x = 3.274823935 Simplifying x = 3.274823935Subproblem 2
x + -1.5 = -1.774823935 Simplifying x + -1.5 = -1.774823935 Reorder the terms: -1.5 + x = -1.774823935 Solving -1.5 + x = -1.774823935 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -1.774823935 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -1.774823935 + 1.5 x = -1.774823935 + 1.5 Combine like terms: -1.774823935 + 1.5 = -0.274823935 x = -0.274823935 Simplifying x = -0.274823935Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.274823935, -0.274823935}
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