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Simplifying x2 + 1.8x = 0.3384 Reorder the terms: 1.8x + x2 = 0.3384 Solving 1.8x + x2 = 0.3384 Solving for variable 'x'. Reorder the terms: -0.3384 + 1.8x + x2 = 0.3384 + -0.3384 Combine like terms: 0.3384 + -0.3384 = 0.0000 -0.3384 + 1.8x + x2 = 0.0000 Begin completing the square. Move the constant term to the right: Add '0.3384' to each side of the equation. -0.3384 + 1.8x + 0.3384 + x2 = 0.0000 + 0.3384 Reorder the terms: -0.3384 + 0.3384 + 1.8x + x2 = 0.0000 + 0.3384 Combine like terms: -0.3384 + 0.3384 = 0.0000 0.0000 + 1.8x + x2 = 0.0000 + 0.3384 1.8x + x2 = 0.0000 + 0.3384 Combine like terms: 0.0000 + 0.3384 = 0.3384 1.8x + x2 = 0.3384 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 = 0.3384 + 0.81 Reorder the terms: 0.81 + 1.8x + x2 = 0.3384 + 0.81 Combine like terms: 0.3384 + 0.81 = 1.1484 0.81 + 1.8x + x2 = 1.1484 Factor a perfect square on the left side: (x + 0.9)(x + 0.9) = 1.1484 Calculate the square root of the right side: 1.071634266 Break this problem into two subproblems by setting (x + 0.9) equal to 1.071634266 and -1.071634266.Subproblem 1
x + 0.9 = 1.071634266 Simplifying x + 0.9 = 1.071634266 Reorder the terms: 0.9 + x = 1.071634266 Solving 0.9 + x = 1.071634266 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 = 1.071634266 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = 1.071634266 + -0.9 x = 1.071634266 + -0.9 Combine like terms: 1.071634266 + -0.9 = 0.171634266 x = 0.171634266 Simplifying x = 0.171634266Subproblem 2
x + 0.9 = -1.071634266 Simplifying x + 0.9 = -1.071634266 Reorder the terms: 0.9 + x = -1.071634266 Solving 0.9 + x = -1.071634266 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 = -1.071634266 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = -1.071634266 + -0.9 x = -1.071634266 + -0.9 Combine like terms: -1.071634266 + -0.9 = -1.971634266 x = -1.971634266 Simplifying x = -1.971634266Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.171634266, -1.971634266}
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