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Simplifying x2 + -44x + 476 = 0 Reorder the terms: 476 + -44x + x2 = 0 Solving 476 + -44x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-476' to each side of the equation. 476 + -44x + -476 + x2 = 0 + -476 Reorder the terms: 476 + -476 + -44x + x2 = 0 + -476 Combine like terms: 476 + -476 = 0 0 + -44x + x2 = 0 + -476 -44x + x2 = 0 + -476 Combine like terms: 0 + -476 = -476 -44x + x2 = -476 The x term is -44x. Take half its coefficient (-22). Square it (484) and add it to both sides. Add '484' to each side of the equation. -44x + 484 + x2 = -476 + 484 Reorder the terms: 484 + -44x + x2 = -476 + 484 Combine like terms: -476 + 484 = 8 484 + -44x + x2 = 8 Factor a perfect square on the left side: (x + -22)(x + -22) = 8 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting (x + -22) equal to 2.828427125 and -2.828427125.Subproblem 1
x + -22 = 2.828427125 Simplifying x + -22 = 2.828427125 Reorder the terms: -22 + x = 2.828427125 Solving -22 + x = 2.828427125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22' to each side of the equation. -22 + 22 + x = 2.828427125 + 22 Combine like terms: -22 + 22 = 0 0 + x = 2.828427125 + 22 x = 2.828427125 + 22 Combine like terms: 2.828427125 + 22 = 24.828427125 x = 24.828427125 Simplifying x = 24.828427125Subproblem 2
x + -22 = -2.828427125 Simplifying x + -22 = -2.828427125 Reorder the terms: -22 + x = -2.828427125 Solving -22 + x = -2.828427125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22' to each side of the equation. -22 + 22 + x = -2.828427125 + 22 Combine like terms: -22 + 22 = 0 0 + x = -2.828427125 + 22 x = -2.828427125 + 22 Combine like terms: -2.828427125 + 22 = 19.171572875 x = 19.171572875 Simplifying x = 19.171572875Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.828427125, 19.171572875}
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