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Simplifying 448x + 8 = 448 + x2 Reorder the terms: 8 + 448x = 448 + x2 Solving 8 + 448x = 448 + x2 Solving for variable 'x'. Reorder the terms: 8 + -448 + 448x + -1x2 = 448 + x2 + -448 + -1x2 Combine like terms: 8 + -448 = -440 -440 + 448x + -1x2 = 448 + x2 + -448 + -1x2 Reorder the terms: -440 + 448x + -1x2 = 448 + -448 + x2 + -1x2 Combine like terms: 448 + -448 = 0 -440 + 448x + -1x2 = 0 + x2 + -1x2 -440 + 448x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -440 + 448x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 440 + -448x + x2 = 0 Move the constant term to the right: Add '-440' to each side of the equation. 440 + -448x + -440 + x2 = 0 + -440 Reorder the terms: 440 + -440 + -448x + x2 = 0 + -440 Combine like terms: 440 + -440 = 0 0 + -448x + x2 = 0 + -440 -448x + x2 = 0 + -440 Combine like terms: 0 + -440 = -440 -448x + x2 = -440 The x term is -448x. Take half its coefficient (-224). Square it (50176) and add it to both sides. Add '50176' to each side of the equation. -448x + 50176 + x2 = -440 + 50176 Reorder the terms: 50176 + -448x + x2 = -440 + 50176 Combine like terms: -440 + 50176 = 49736 50176 + -448x + x2 = 49736 Factor a perfect square on the left side: (x + -224)(x + -224) = 49736 Calculate the square root of the right side: 223.015694515 Break this problem into two subproblems by setting (x + -224) equal to 223.015694515 and -223.015694515.Subproblem 1
x + -224 = 223.015694515 Simplifying x + -224 = 223.015694515 Reorder the terms: -224 + x = 223.015694515 Solving -224 + x = 223.015694515 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '224' to each side of the equation. -224 + 224 + x = 223.015694515 + 224 Combine like terms: -224 + 224 = 0 0 + x = 223.015694515 + 224 x = 223.015694515 + 224 Combine like terms: 223.015694515 + 224 = 447.015694515 x = 447.015694515 Simplifying x = 447.015694515Subproblem 2
x + -224 = -223.015694515 Simplifying x + -224 = -223.015694515 Reorder the terms: -224 + x = -223.015694515 Solving -224 + x = -223.015694515 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '224' to each side of the equation. -224 + 224 + x = -223.015694515 + 224 Combine like terms: -224 + 224 = 0 0 + x = -223.015694515 + 224 x = -223.015694515 + 224 Combine like terms: -223.015694515 + 224 = 0.984305485 x = 0.984305485 Simplifying x = 0.984305485Solution
The solution to the problem is based on the solutions from the subproblems. x = {447.015694515, 0.984305485}
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