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Simplifying x2 + -40x + 148 = 0 Reorder the terms: 148 + -40x + x2 = 0 Solving 148 + -40x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-148' to each side of the equation. 148 + -40x + -148 + x2 = 0 + -148 Reorder the terms: 148 + -148 + -40x + x2 = 0 + -148 Combine like terms: 148 + -148 = 0 0 + -40x + x2 = 0 + -148 -40x + x2 = 0 + -148 Combine like terms: 0 + -148 = -148 -40x + x2 = -148 The x term is -40x. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40x + 400 + x2 = -148 + 400 Reorder the terms: 400 + -40x + x2 = -148 + 400 Combine like terms: -148 + 400 = 252 400 + -40x + x2 = 252 Factor a perfect square on the left side: (x + -20)(x + -20) = 252 Calculate the square root of the right side: 15.874507866 Break this problem into two subproblems by setting (x + -20) equal to 15.874507866 and -15.874507866.Subproblem 1
x + -20 = 15.874507866 Simplifying x + -20 = 15.874507866 Reorder the terms: -20 + x = 15.874507866 Solving -20 + x = 15.874507866 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = 15.874507866 + 20 Combine like terms: -20 + 20 = 0 0 + x = 15.874507866 + 20 x = 15.874507866 + 20 Combine like terms: 15.874507866 + 20 = 35.874507866 x = 35.874507866 Simplifying x = 35.874507866Subproblem 2
x + -20 = -15.874507866 Simplifying x + -20 = -15.874507866 Reorder the terms: -20 + x = -15.874507866 Solving -20 + x = -15.874507866 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = -15.874507866 + 20 Combine like terms: -20 + 20 = 0 0 + x = -15.874507866 + 20 x = -15.874507866 + 20 Combine like terms: -15.874507866 + 20 = 4.125492134 x = 4.125492134 Simplifying x = 4.125492134Solution
The solution to the problem is based on the solutions from the subproblems. x = {35.874507866, 4.125492134}
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