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Simplifying x2 = 30x + 27 Reorder the terms: x2 = 27 + 30x Solving x2 = 27 + 30x Solving for variable 'x'. Reorder the terms: -27 + -30x + x2 = 27 + 30x + -27 + -30x Reorder the terms: -27 + -30x + x2 = 27 + -27 + 30x + -30x Combine like terms: 27 + -27 = 0 -27 + -30x + x2 = 0 + 30x + -30x -27 + -30x + x2 = 30x + -30x Combine like terms: 30x + -30x = 0 -27 + -30x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '27' to each side of the equation. -27 + -30x + 27 + x2 = 0 + 27 Reorder the terms: -27 + 27 + -30x + x2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + -30x + x2 = 0 + 27 -30x + x2 = 0 + 27 Combine like terms: 0 + 27 = 27 -30x + x2 = 27 The x term is -30x. Take half its coefficient (-15). Square it (225) and add it to both sides. Add '225' to each side of the equation. -30x + 225 + x2 = 27 + 225 Reorder the terms: 225 + -30x + x2 = 27 + 225 Combine like terms: 27 + 225 = 252 225 + -30x + x2 = 252 Factor a perfect square on the left side: (x + -15)(x + -15) = 252 Calculate the square root of the right side: 15.874507866 Break this problem into two subproblems by setting (x + -15) equal to 15.874507866 and -15.874507866.Subproblem 1
x + -15 = 15.874507866 Simplifying x + -15 = 15.874507866 Reorder the terms: -15 + x = 15.874507866 Solving -15 + x = 15.874507866 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = 15.874507866 + 15 Combine like terms: -15 + 15 = 0 0 + x = 15.874507866 + 15 x = 15.874507866 + 15 Combine like terms: 15.874507866 + 15 = 30.874507866 x = 30.874507866 Simplifying x = 30.874507866Subproblem 2
x + -15 = -15.874507866 Simplifying x + -15 = -15.874507866 Reorder the terms: -15 + x = -15.874507866 Solving -15 + x = -15.874507866 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = -15.874507866 + 15 Combine like terms: -15 + 15 = 0 0 + x = -15.874507866 + 15 x = -15.874507866 + 15 Combine like terms: -15.874507866 + 15 = -0.874507866 x = -0.874507866 Simplifying x = -0.874507866Solution
The solution to the problem is based on the solutions from the subproblems. x = {30.874507866, -0.874507866}
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