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Simplifying 27 = 100x + -2x2 Solving 27 = 100x + -2x2 Solving for variable 'x'. Reorder the terms: 27 + -100x + 2x2 = 100x + -100x + -2x2 + 2x2 Combine like terms: 100x + -100x = 0 27 + -100x + 2x2 = 0 + -2x2 + 2x2 27 + -100x + 2x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 27 + -100x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 13.5 + -50x + x2 = 0 Move the constant term to the right: Add '-13.5' to each side of the equation. 13.5 + -50x + -13.5 + x2 = 0 + -13.5 Reorder the terms: 13.5 + -13.5 + -50x + x2 = 0 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + -50x + x2 = 0 + -13.5 -50x + x2 = 0 + -13.5 Combine like terms: 0 + -13.5 = -13.5 -50x + x2 = -13.5 The x term is -50x. Take half its coefficient (-25). Square it (625) and add it to both sides. Add '625' to each side of the equation. -50x + 625 + x2 = -13.5 + 625 Reorder the terms: 625 + -50x + x2 = -13.5 + 625 Combine like terms: -13.5 + 625 = 611.5 625 + -50x + x2 = 611.5 Factor a perfect square on the left side: (x + -25)(x + -25) = 611.5 Calculate the square root of the right side: 24.728526038 Break this problem into two subproblems by setting (x + -25) equal to 24.728526038 and -24.728526038.Subproblem 1
x + -25 = 24.728526038 Simplifying x + -25 = 24.728526038 Reorder the terms: -25 + x = 24.728526038 Solving -25 + x = 24.728526038 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = 24.728526038 + 25 Combine like terms: -25 + 25 = 0 0 + x = 24.728526038 + 25 x = 24.728526038 + 25 Combine like terms: 24.728526038 + 25 = 49.728526038 x = 49.728526038 Simplifying x = 49.728526038Subproblem 2
x + -25 = -24.728526038 Simplifying x + -25 = -24.728526038 Reorder the terms: -25 + x = -24.728526038 Solving -25 + x = -24.728526038 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = -24.728526038 + 25 Combine like terms: -25 + 25 = 0 0 + x = -24.728526038 + 25 x = -24.728526038 + 25 Combine like terms: -24.728526038 + 25 = 0.271473962 x = 0.271473962 Simplifying x = 0.271473962Solution
The solution to the problem is based on the solutions from the subproblems. x = {49.728526038, 0.271473962}
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