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Simplifying 5x2 = 2.2x2 + 5.88x + 3.168 Reorder the terms: 5x2 = 3.168 + 5.88x + 2.2x2 Solving 5x2 = 3.168 + 5.88x + 2.2x2 Solving for variable 'x'. Reorder the terms: -3.168 + -5.88x + 5x2 + -2.2x2 = 3.168 + 5.88x + 2.2x2 + -3.168 + -5.88x + -2.2x2 Combine like terms: 5x2 + -2.2x2 = 2.8x2 -3.168 + -5.88x + 2.8x2 = 3.168 + 5.88x + 2.2x2 + -3.168 + -5.88x + -2.2x2 Reorder the terms: -3.168 + -5.88x + 2.8x2 = 3.168 + -3.168 + 5.88x + -5.88x + 2.2x2 + -2.2x2 Combine like terms: 3.168 + -3.168 = 0.000 -3.168 + -5.88x + 2.8x2 = 0.000 + 5.88x + -5.88x + 2.2x2 + -2.2x2 -3.168 + -5.88x + 2.8x2 = 5.88x + -5.88x + 2.2x2 + -2.2x2 Combine like terms: 5.88x + -5.88x = 0.00 -3.168 + -5.88x + 2.8x2 = 0.00 + 2.2x2 + -2.2x2 -3.168 + -5.88x + 2.8x2 = 2.2x2 + -2.2x2 Combine like terms: 2.2x2 + -2.2x2 = 0.0 -3.168 + -5.88x + 2.8x2 = 0.0 Begin completing the square. Divide all terms by 2.8 the coefficient of the squared term: Divide each side by '2.8'. -1.131428571 + -2.1x + x2 = 0 Move the constant term to the right: Add '1.131428571' to each side of the equation. -1.131428571 + -2.1x + 1.131428571 + x2 = 0 + 1.131428571 Reorder the terms: -1.131428571 + 1.131428571 + -2.1x + x2 = 0 + 1.131428571 Combine like terms: -1.131428571 + 1.131428571 = 0.000000000 0.000000000 + -2.1x + x2 = 0 + 1.131428571 -2.1x + x2 = 0 + 1.131428571 Combine like terms: 0 + 1.131428571 = 1.131428571 -2.1x + x2 = 1.131428571 The x term is -2.1x. Take half its coefficient (-1.05). Square it (1.1025) and add it to both sides. Add '1.1025' to each side of the equation. -2.1x + 1.1025 + x2 = 1.131428571 + 1.1025 Reorder the terms: 1.1025 + -2.1x + x2 = 1.131428571 + 1.1025 Combine like terms: 1.131428571 + 1.1025 = 2.233928571 1.1025 + -2.1x + x2 = 2.233928571 Factor a perfect square on the left side: (x + -1.05)(x + -1.05) = 2.233928571 Calculate the square root of the right side: 1.494633256 Break this problem into two subproblems by setting (x + -1.05) equal to 1.494633256 and -1.494633256.Subproblem 1
x + -1.05 = 1.494633256 Simplifying x + -1.05 = 1.494633256 Reorder the terms: -1.05 + x = 1.494633256 Solving -1.05 + x = 1.494633256 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.05' to each side of the equation. -1.05 + 1.05 + x = 1.494633256 + 1.05 Combine like terms: -1.05 + 1.05 = 0.00 0.00 + x = 1.494633256 + 1.05 x = 1.494633256 + 1.05 Combine like terms: 1.494633256 + 1.05 = 2.544633256 x = 2.544633256 Simplifying x = 2.544633256Subproblem 2
x + -1.05 = -1.494633256 Simplifying x + -1.05 = -1.494633256 Reorder the terms: -1.05 + x = -1.494633256 Solving -1.05 + x = -1.494633256 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.05' to each side of the equation. -1.05 + 1.05 + x = -1.494633256 + 1.05 Combine like terms: -1.05 + 1.05 = 0.00 0.00 + x = -1.494633256 + 1.05 x = -1.494633256 + 1.05 Combine like terms: -1.494633256 + 1.05 = -0.444633256 x = -0.444633256 Simplifying x = -0.444633256Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.544633256, -0.444633256}
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