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Simplifying 412 = 0.054x2 + 1.1x Reorder the terms: 412 = 1.1x + 0.054x2 Solving 412 = 1.1x + 0.054x2 Solving for variable 'x'. Reorder the terms: 412 + -1.1x + -0.054x2 = 1.1x + -1.1x + 0.054x2 + -0.054x2 Combine like terms: 1.1x + -1.1x = 0.0 412 + -1.1x + -0.054x2 = 0.0 + 0.054x2 + -0.054x2 412 + -1.1x + -0.054x2 = 0.054x2 + -0.054x2 Combine like terms: 0.054x2 + -0.054x2 = 0.000 412 + -1.1x + -0.054x2 = 0.000 Begin completing the square. Divide all terms by -0.054 the coefficient of the squared term: Divide each side by '-0.054'. -7629.62963 + 20.37037037x + x2 = 0 Move the constant term to the right: Add '7629.62963' to each side of the equation. -7629.62963 + 20.37037037x + 7629.62963 + x2 = 0 + 7629.62963 Reorder the terms: -7629.62963 + 7629.62963 + 20.37037037x + x2 = 0 + 7629.62963 Combine like terms: -7629.62963 + 7629.62963 = 0.00000 0.00000 + 20.37037037x + x2 = 0 + 7629.62963 20.37037037x + x2 = 0 + 7629.62963 Combine like terms: 0 + 7629.62963 = 7629.62963 20.37037037x + x2 = 7629.62963 The x term is 20.37037037x. Take half its coefficient (10.18518519). Square it (103.7379974) and add it to both sides. Add '103.7379974' to each side of the equation. 20.37037037x + 103.7379974 + x2 = 7629.62963 + 103.7379974 Reorder the terms: 103.7379974 + 20.37037037x + x2 = 7629.62963 + 103.7379974 Combine like terms: 7629.62963 + 103.7379974 = 7733.3676274 103.7379974 + 20.37037037x + x2 = 7733.3676274 Factor a perfect square on the left side: (x + 10.18518519)(x + 10.18518519) = 7733.3676274 Calculate the square root of the right side: 87.939568042 Break this problem into two subproblems by setting (x + 10.18518519) equal to 87.939568042 and -87.939568042.Subproblem 1
x + 10.18518519 = 87.939568042 Simplifying x + 10.18518519 = 87.939568042 Reorder the terms: 10.18518519 + x = 87.939568042 Solving 10.18518519 + x = 87.939568042 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.18518519' to each side of the equation. 10.18518519 + -10.18518519 + x = 87.939568042 + -10.18518519 Combine like terms: 10.18518519 + -10.18518519 = 0.00000000 0.00000000 + x = 87.939568042 + -10.18518519 x = 87.939568042 + -10.18518519 Combine like terms: 87.939568042 + -10.18518519 = 77.754382852 x = 77.754382852 Simplifying x = 77.754382852Subproblem 2
x + 10.18518519 = -87.939568042 Simplifying x + 10.18518519 = -87.939568042 Reorder the terms: 10.18518519 + x = -87.939568042 Solving 10.18518519 + x = -87.939568042 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.18518519' to each side of the equation. 10.18518519 + -10.18518519 + x = -87.939568042 + -10.18518519 Combine like terms: 10.18518519 + -10.18518519 = 0.00000000 0.00000000 + x = -87.939568042 + -10.18518519 x = -87.939568042 + -10.18518519 Combine like terms: -87.939568042 + -10.18518519 = -98.124753232 x = -98.124753232 Simplifying x = -98.124753232Solution
The solution to the problem is based on the solutions from the subproblems. x = {77.754382852, -98.124753232}
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