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Simplifying x2 + -25x + 4x = 52 Reorder the terms: -25x + 4x + x2 = 52 Combine like terms: -25x + 4x = -21x -21x + x2 = 52 Solving -21x + x2 = 52 Solving for variable 'x'. Reorder the terms: -52 + -21x + x2 = 52 + -52 Combine like terms: 52 + -52 = 0 -52 + -21x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '52' to each side of the equation. -52 + -21x + 52 + x2 = 0 + 52 Reorder the terms: -52 + 52 + -21x + x2 = 0 + 52 Combine like terms: -52 + 52 = 0 0 + -21x + x2 = 0 + 52 -21x + x2 = 0 + 52 Combine like terms: 0 + 52 = 52 -21x + x2 = 52 The x term is -21x. Take half its coefficient (-10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. -21x + 110.25 + x2 = 52 + 110.25 Reorder the terms: 110.25 + -21x + x2 = 52 + 110.25 Combine like terms: 52 + 110.25 = 162.25 110.25 + -21x + x2 = 162.25 Factor a perfect square on the left side: (x + -10.5)(x + -10.5) = 162.25 Calculate the square root of the right side: 12.737739203 Break this problem into two subproblems by setting (x + -10.5) equal to 12.737739203 and -12.737739203.Subproblem 1
x + -10.5 = 12.737739203 Simplifying x + -10.5 = 12.737739203 Reorder the terms: -10.5 + x = 12.737739203 Solving -10.5 + x = 12.737739203 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + x = 12.737739203 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = 12.737739203 + 10.5 x = 12.737739203 + 10.5 Combine like terms: 12.737739203 + 10.5 = 23.237739203 x = 23.237739203 Simplifying x = 23.237739203Subproblem 2
x + -10.5 = -12.737739203 Simplifying x + -10.5 = -12.737739203 Reorder the terms: -10.5 + x = -12.737739203 Solving -10.5 + x = -12.737739203 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + x = -12.737739203 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = -12.737739203 + 10.5 x = -12.737739203 + 10.5 Combine like terms: -12.737739203 + 10.5 = -2.237739203 x = -2.237739203 Simplifying x = -2.237739203Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.237739203, -2.237739203}
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