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Simplifying (X + -0.92)(X + -0.92) = 0 Reorder the terms: (-0.92 + X)(X + -0.92) = 0 Reorder the terms: (-0.92 + X)(-0.92 + X) = 0 Multiply (-0.92 + X) * (-0.92 + X) (-0.92(-0.92 + X) + X(-0.92 + X)) = 0 ((-0.92 * -0.92 + X * -0.92) + X(-0.92 + X)) = 0 ((0.8464 + -0.92X) + X(-0.92 + X)) = 0 (0.8464 + -0.92X + (-0.92 * X + X * X)) = 0 (0.8464 + -0.92X + (-0.92X + X2)) = 0 Combine like terms: -0.92X + -0.92X = -1.84X (0.8464 + -1.84X + X2) = 0 Solving 0.8464 + -1.84X + X2 = 0 Solving for variable 'X'. Begin completing the square. Move the constant term to the right: Add '-0.8464' to each side of the equation. 0.8464 + -1.84X + -0.8464 + X2 = 0 + -0.8464 Reorder the terms: 0.8464 + -0.8464 + -1.84X + X2 = 0 + -0.8464 Combine like terms: 0.8464 + -0.8464 = 0.0000 0.0000 + -1.84X + X2 = 0 + -0.8464 -1.84X + X2 = 0 + -0.8464 Combine like terms: 0 + -0.8464 = -0.8464 -1.84X + X2 = -0.8464 The X term is -1.84X. Take half its coefficient (-0.92). Square it (0.8464) and add it to both sides. Add '0.8464' to each side of the equation. -1.84X + 0.8464 + X2 = -0.8464 + 0.8464 Reorder the terms: 0.8464 + -1.84X + X2 = -0.8464 + 0.8464 Combine like terms: -0.8464 + 0.8464 = 0.0000 0.8464 + -1.84X + X2 = 0.0000 Factor a perfect square on the left side: (X + -0.92)(X + -0.92) = 0.0000 Calculate the square root of the right side: 0.0000 Break this problem into two subproblems by setting (X + -0.92) equal to 0.0000 and 0.0000.Subproblem 1
X + -0.92 = 0.0000 Simplifying X + -0.92 = 0.0000 Reorder the terms: -0.92 + X = 0.0000 Solving -0.92 + X = 0.0000 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.92' to each side of the equation. -0.92 + 0.92 + X = 0.0000 + 0.92 Combine like terms: -0.92 + 0.92 = 0.00 0.00 + X = 0.0000 + 0.92 X = 0.0000 + 0.92 Combine like terms: 0.0000 + 0.92 = 0.92 X = 0.92 Simplifying X = 0.92Subproblem 2
X + -0.92 = 0.0000 Simplifying X + -0.92 = 0.0000 Reorder the terms: -0.92 + X = 0.0000 Solving -0.92 + X = 0.0000 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.92' to each side of the equation. -0.92 + 0.92 + X = 0.0000 + 0.92 Combine like terms: -0.92 + 0.92 = 0.00 0.00 + X = 0.0000 + 0.92 X = 0.0000 + 0.92 Combine like terms: 0.0000 + 0.92 = 0.92 X = 0.92 Simplifying X = 0.92Solution
The solution to the problem is based on the solutions from the subproblems. X = {0.92, 0.92}
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