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Simplifying x2 + -4.8x + 5.2 = 0 Reorder the terms: 5.2 + -4.8x + x2 = 0 Solving 5.2 + -4.8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-5.2' to each side of the equation. 5.2 + -4.8x + -5.2 + x2 = 0 + -5.2 Reorder the terms: 5.2 + -5.2 + -4.8x + x2 = 0 + -5.2 Combine like terms: 5.2 + -5.2 = 0.0 0.0 + -4.8x + x2 = 0 + -5.2 -4.8x + x2 = 0 + -5.2 Combine like terms: 0 + -5.2 = -5.2 -4.8x + x2 = -5.2 The x term is -4.8x. Take half its coefficient (-2.4). Square it (5.76) and add it to both sides. Add '5.76' to each side of the equation. -4.8x + 5.76 + x2 = -5.2 + 5.76 Reorder the terms: 5.76 + -4.8x + x2 = -5.2 + 5.76 Combine like terms: -5.2 + 5.76 = 0.56 5.76 + -4.8x + x2 = 0.56 Factor a perfect square on the left side: (x + -2.4)(x + -2.4) = 0.56 Calculate the square root of the right side: 0.748331477 Break this problem into two subproblems by setting (x + -2.4) equal to 0.748331477 and -0.748331477.Subproblem 1
x + -2.4 = 0.748331477 Simplifying x + -2.4 = 0.748331477 Reorder the terms: -2.4 + x = 0.748331477 Solving -2.4 + x = 0.748331477 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.4' to each side of the equation. -2.4 + 2.4 + x = 0.748331477 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + x = 0.748331477 + 2.4 x = 0.748331477 + 2.4 Combine like terms: 0.748331477 + 2.4 = 3.148331477 x = 3.148331477 Simplifying x = 3.148331477Subproblem 2
x + -2.4 = -0.748331477 Simplifying x + -2.4 = -0.748331477 Reorder the terms: -2.4 + x = -0.748331477 Solving -2.4 + x = -0.748331477 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.4' to each side of the equation. -2.4 + 2.4 + x = -0.748331477 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + x = -0.748331477 + 2.4 x = -0.748331477 + 2.4 Combine like terms: -0.748331477 + 2.4 = 1.651668523 x = 1.651668523 Simplifying x = 1.651668523Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.148331477, 1.651668523}
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