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Simplifying x2 + -8.8x + 7 = 0 Reorder the terms: 7 + -8.8x + x2 = 0 Solving 7 + -8.8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + -8.8x + -7 + x2 = 0 + -7 Reorder the terms: 7 + -7 + -8.8x + x2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -8.8x + x2 = 0 + -7 -8.8x + x2 = 0 + -7 Combine like terms: 0 + -7 = -7 -8.8x + x2 = -7 The x term is -8.8x. Take half its coefficient (-4.4). Square it (19.36) and add it to both sides. Add '19.36' to each side of the equation. -8.8x + 19.36 + x2 = -7 + 19.36 Reorder the terms: 19.36 + -8.8x + x2 = -7 + 19.36 Combine like terms: -7 + 19.36 = 12.36 19.36 + -8.8x + x2 = 12.36 Factor a perfect square on the left side: (x + -4.4)(x + -4.4) = 12.36 Calculate the square root of the right side: 3.515679166 Break this problem into two subproblems by setting (x + -4.4) equal to 3.515679166 and -3.515679166.Subproblem 1
x + -4.4 = 3.515679166 Simplifying x + -4.4 = 3.515679166 Reorder the terms: -4.4 + x = 3.515679166 Solving -4.4 + x = 3.515679166 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.4' to each side of the equation. -4.4 + 4.4 + x = 3.515679166 + 4.4 Combine like terms: -4.4 + 4.4 = 0.0 0.0 + x = 3.515679166 + 4.4 x = 3.515679166 + 4.4 Combine like terms: 3.515679166 + 4.4 = 7.915679166 x = 7.915679166 Simplifying x = 7.915679166Subproblem 2
x + -4.4 = -3.515679166 Simplifying x + -4.4 = -3.515679166 Reorder the terms: -4.4 + x = -3.515679166 Solving -4.4 + x = -3.515679166 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.4' to each side of the equation. -4.4 + 4.4 + x = -3.515679166 + 4.4 Combine like terms: -4.4 + 4.4 = 0.0 0.0 + x = -3.515679166 + 4.4 x = -3.515679166 + 4.4 Combine like terms: -3.515679166 + 4.4 = 0.884320834 x = 0.884320834 Simplifying x = 0.884320834Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.915679166, 0.884320834}
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