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Simplifying x2 + -5.8x = -7.1 Reorder the terms: -5.8x + x2 = -7.1 Solving -5.8x + x2 = -7.1 Solving for variable 'x'. Reorder the terms: 7.1 + -5.8x + x2 = -7.1 + 7.1 Combine like terms: -7.1 + 7.1 = 0.0 7.1 + -5.8x + x2 = 0.0 Begin completing the square. Move the constant term to the right: Add '-7.1' to each side of the equation. 7.1 + -5.8x + -7.1 + x2 = 0.0 + -7.1 Reorder the terms: 7.1 + -7.1 + -5.8x + x2 = 0.0 + -7.1 Combine like terms: 7.1 + -7.1 = 0.0 0.0 + -5.8x + x2 = 0.0 + -7.1 -5.8x + x2 = 0.0 + -7.1 Combine like terms: 0.0 + -7.1 = -7.1 -5.8x + x2 = -7.1 The x term is -5.8x. Take half its coefficient (-2.9). Square it (8.41) and add it to both sides. Add '8.41' to each side of the equation. -5.8x + 8.41 + x2 = -7.1 + 8.41 Reorder the terms: 8.41 + -5.8x + x2 = -7.1 + 8.41 Combine like terms: -7.1 + 8.41 = 1.31 8.41 + -5.8x + x2 = 1.31 Factor a perfect square on the left side: (x + -2.9)(x + -2.9) = 1.31 Calculate the square root of the right side: 1.144552314 Break this problem into two subproblems by setting (x + -2.9) equal to 1.144552314 and -1.144552314.Subproblem 1
x + -2.9 = 1.144552314 Simplifying x + -2.9 = 1.144552314 Reorder the terms: -2.9 + x = 1.144552314 Solving -2.9 + x = 1.144552314 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.9' to each side of the equation. -2.9 + 2.9 + x = 1.144552314 + 2.9 Combine like terms: -2.9 + 2.9 = 0.0 0.0 + x = 1.144552314 + 2.9 x = 1.144552314 + 2.9 Combine like terms: 1.144552314 + 2.9 = 4.044552314 x = 4.044552314 Simplifying x = 4.044552314Subproblem 2
x + -2.9 = -1.144552314 Simplifying x + -2.9 = -1.144552314 Reorder the terms: -2.9 + x = -1.144552314 Solving -2.9 + x = -1.144552314 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.9' to each side of the equation. -2.9 + 2.9 + x = -1.144552314 + 2.9 Combine like terms: -2.9 + 2.9 = 0.0 0.0 + x = -1.144552314 + 2.9 x = -1.144552314 + 2.9 Combine like terms: -1.144552314 + 2.9 = 1.755447686 x = 1.755447686 Simplifying x = 1.755447686Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.044552314, 1.755447686}
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