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Simplifying x2 + 36 = 25x Reorder the terms: 36 + x2 = 25x Solving 36 + x2 = 25x Solving for variable 'x'. Reorder the terms: 36 + -25x + x2 = 25x + -25x Combine like terms: 25x + -25x = 0 36 + -25x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-36' to each side of the equation. 36 + -25x + -36 + x2 = 0 + -36 Reorder the terms: 36 + -36 + -25x + x2 = 0 + -36 Combine like terms: 36 + -36 = 0 0 + -25x + x2 = 0 + -36 -25x + x2 = 0 + -36 Combine like terms: 0 + -36 = -36 -25x + x2 = -36 The x term is -25x. Take half its coefficient (-12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. -25x + 156.25 + x2 = -36 + 156.25 Reorder the terms: 156.25 + -25x + x2 = -36 + 156.25 Combine like terms: -36 + 156.25 = 120.25 156.25 + -25x + x2 = 120.25 Factor a perfect square on the left side: (x + -12.5)(x + -12.5) = 120.25 Calculate the square root of the right side: 10.9658561 Break this problem into two subproblems by setting (x + -12.5) equal to 10.9658561 and -10.9658561.Subproblem 1
x + -12.5 = 10.9658561 Simplifying x + -12.5 = 10.9658561 Reorder the terms: -12.5 + x = 10.9658561 Solving -12.5 + x = 10.9658561 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + x = 10.9658561 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = 10.9658561 + 12.5 x = 10.9658561 + 12.5 Combine like terms: 10.9658561 + 12.5 = 23.4658561 x = 23.4658561 Simplifying x = 23.4658561Subproblem 2
x + -12.5 = -10.9658561 Simplifying x + -12.5 = -10.9658561 Reorder the terms: -12.5 + x = -10.9658561 Solving -12.5 + x = -10.9658561 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + x = -10.9658561 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = -10.9658561 + 12.5 x = -10.9658561 + 12.5 Combine like terms: -10.9658561 + 12.5 = 1.5341439 x = 1.5341439 Simplifying x = 1.5341439Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.4658561, 1.5341439}
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