(10÷5x-21 +5x-21÷10) ^2=25÷4

To solve this equation, we need to follow the order of operations (PEMDAS/BODMAS). First, let's simplify the expression inside the parentheses: 10 ÷ 5x - 21 + 5x - 21 ÷ 10 Next, let's simplify the terms within the expression: 10 ÷ 5x is the same as 2 ÷ x -21 ÷ 10 is the same as -2.1 So, the expression becomes: 2 ÷ x + 5x - 2.1 Now, let's rewrite the equation with the simplified expression: (2 ÷ x + 5x - 2.1) ^ 2 = 25 ÷ 4 Next, let's square both sides of the equation: (2 ÷ x + 5x - 2.1) ^ 2 = (5/2) ^ 2 Squaring the left side: (2 ÷ x + 5x - 2.1) * (2 ÷ x + 5x - 2.1) = 25/4 Expanding the left side of the equation: 4 ÷ x^2 + 10x ÷ x + 4(5x) - 4(2.1) + 10x^2 ÷ x - 21x + 2.1x + 5x - 21 = 25/4 Simplifying the equation: 4/x^2 + 10 + 20x - 8.4 + 10x - 21x + 2.1x + 5x - 21 = 25/4 Combining like terms on the left side: 4/x^2 + 18.1x - 21 = 25/4 Multiplying both sides by 4: 4(4/x^2 + 18.1x - 21) = 25 Expanding the left side: 16/x^2 + 72.4x - 84 = 25 Next, let's bring 25 to the left side: 16/x^2 + 72.4x - 84 - 25 = 0 Combine like terms: 16/x^2 + 72.4x - 109 = 0 Now, this equation can be solved using various algebraic methods, such as factoring, quadratic formula, or graphing.