The solution of the equation, 2 x = − 5 x + 24 − 3 and check the solution. The solution of the given equation, 2 x = − 5 x + 24 − 3 is x = 3 4 . Calculation: Consider the provided equation, 2 x = − 5 x + 24 − 3 Isolate the radical. 2 x + 3 = − 5 x + 24 Square each side and solve. 2 x + 3 2 = − 5 x + 24 9 + 4 x 2 + 12 x = − 5 x + 24 Write the above equation in standard form. 4 x 2 + 17 x − 15 = 0 Now factorize the above equation. 4 x − 3 x + 5 = 0 Put the first factor equal to zero. 4 x − 3 = 0 x = 3 4 Put the second factor equal to zero. x + 5 = 0 x = − 5 Check: Put x = 3 4 , − 5 in the equation, 2 x = − 5 x + 24 − 3 . First put x = 3 4 . 2 3 4 = ? − 5 3 4 + 24 − 3 3 2 = ? − 15 4 + 24 − 3 3 2 = ? 81 4 − 3 3 2 = 3 2 Which is true. Now put x = − 5 . 2 − 5 = ? − 5 − 5 + 24 − 3 − 10 = ? − 25 + 24 − 3 − 10 = ? − 1 − 3 Which is false, and therefore x = − 5 is not the solution. Hence, the solution of the given equation is x = 3 4 .
The solution of the equation, 2 x = − 5 x + 24 − 3 and check the solution. The solution of the given equation, 2 x = − 5 x + 24 − 3 is x = 3 4 . Calculation: Consider the provided equation, 2 x = − 5 x + 24 − 3 Isolate the radical. 2 x + 3 = − 5 x + 24 Square each side and solve. 2 x + 3 2 = − 5 x + 24 9 + 4 x 2 + 12 x = − 5 x + 24 Write the above equation in standard form. 4 x 2 + 17 x − 15 = 0 Now factorize the above equation. 4 x − 3 x + 5 = 0 Put the first factor equal to zero. 4 x − 3 = 0 x = 3 4 Put the second factor equal to zero. x + 5 = 0 x = − 5 Check: Put x = 3 4 , − 5 in the equation, 2 x = − 5 x + 24 − 3 . First put x = 3 4 . 2 3 4 = ? − 5 3 4 + 24 − 3 3 2 = ? − 15 4 + 24 − 3 3 2 = ? 81 4 − 3 3 2 = 3 2 Which is true. Now put x = − 5 . 2 − 5 = ? − 5 − 5 + 24 − 3 − 10 = ? − 25 + 24 − 3 − 10 = ? − 1 − 3 Which is false, and therefore x = − 5 is not the solution. Hence, the solution of the given equation is x = 3 4 .
Solution Summary: The author calculates the solution of the given equation, 2x=sqrt-5x+24-3.
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