Solve the equation (5)/( x) = 7 - (2 2 x)/( x) for x in the range -90^ x 90^.

You're on a roll — Step 1: Identify the domain and restrictions. The equation involves x in the denominator, so x ≠ 0. This means x ≠ 0^ within the given range of -90^ x 90^. Step 2: Combine the terms on the left side of the equation. (5)/( x) = 7 - (2 ^2 x)/( x) Add (2 ^2 x)/( x) to both sides: (5)/( x) + (2 ^2 x)/( x) = 7 (5 + 2 ^2 x)/( x) = 7 Step 3: Use the trigonometric identity ^2 x = 1 - ^2 x. Substitute this into the equation: (5 + 2(1 - ^2 x))/( x) = 7 (5 + 2 - 2 ^2 x)/( x) = 7 (7 - 2 ^2 x)/( x) = 7 Step 4: Multiply both sides by x. 7 - 2 ^2 x = 7 x Step 5: Rearrange the equation into a quadratic form in terms of x. Move all terms to one side: 2 ^2 x + 7 x - 7 = 0 Step 6: Solve the quadratic equation for x using the quadratic formula y = -b ± sqrt(b^2 - 4ac)2a, where y = x. Here, a=2, b=7, c=-7. x = -7 ± sqrt(7^2 - 4(2)(-7))2(2) x = -7 ± sqrt(49 + 56)4 x = -7 ± sqrt(105)4 Step 7: Calculate the two possible values for x. x_1 = -7 + sqrt(105)4 ≈ (-7 + 10.247)/(4) ≈ (3.247)/(4) ≈ 0.81175 x_2 = -7 - sqrt(105)4 ≈ (-7 - 10.247)/(4) ≈ (-17.247)/(4) ≈ -4.31175 Step 8: Check for valid values of x. The range of x is [-1, 1]. x_1 ≈ 0.81175 is within the valid range. x_2 ≈ -4.31175 is outside the valid range, so this solution is rejected. Step 9: Find the value of x for x = 0.81175 within the given range -90^ x 90^. Since x is positive, x must be in the first quadrant. x = (0.81175) x ≈ 54.26^ This value is within the specified range -90^ x 90^ and satisfies the restriction x ≠ 0^. The solution to the equation is x ≈ 54.26^. Send me the next one 📸