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Simplifying x2 + 1.8x + -5.4 = 0 Reorder the terms: -5.4 + 1.8x + x2 = 0 Solving -5.4 + 1.8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '5.4' to each side of the equation. -5.4 + 1.8x + 5.4 + x2 = 0 + 5.4 Reorder the terms: -5.4 + 5.4 + 1.8x + x2 = 0 + 5.4 Combine like terms: -5.4 + 5.4 = 0.0 0.0 + 1.8x + x2 = 0 + 5.4 1.8x + x2 = 0 + 5.4 Combine like terms: 0 + 5.4 = 5.4 1.8x + x2 = 5.4 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 = 5.4 + 0.81 Reorder the terms: 0.81 + 1.8x + x2 = 5.4 + 0.81 Combine like terms: 5.4 + 0.81 = 6.21 0.81 + 1.8x + x2 = 6.21 Factor a perfect square on the left side: (x + 0.9)(x + 0.9) = 6.21 Calculate the square root of the right side: 2.491987159 Break this problem into two subproblems by setting (x + 0.9) equal to 2.491987159 and -2.491987159.Subproblem 1
x + 0.9 = 2.491987159 Simplifying x + 0.9 = 2.491987159 Reorder the terms: 0.9 + x = 2.491987159 Solving 0.9 + x = 2.491987159 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 = 2.491987159 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = 2.491987159 + -0.9 x = 2.491987159 + -0.9 Combine like terms: 2.491987159 + -0.9 = 1.591987159 x = 1.591987159 Simplifying x = 1.591987159Subproblem 2
x + 0.9 = -2.491987159 Simplifying x + 0.9 = -2.491987159 Reorder the terms: 0.9 + x = -2.491987159 Solving 0.9 + x = -2.491987159 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 = -2.491987159 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = -2.491987159 + -0.9 x = -2.491987159 + -0.9 Combine like terms: -2.491987159 + -0.9 = -3.391987159 x = -3.391987159 Simplifying x = -3.391987159Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.591987159, -3.391987159}
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