Answer :
Final answer:
To solve the equation, distribute the exponent, combine like terms, and solve the resulting quadratic equation.Then we get ,x = 4 and x = -2.
Explanation:
To solve the equation 1/2 x + 7 - ²x = 15, we need to simplify and isolate the variable x. First, distribute the exponent by writing ²x as x^2. Then, combine like terms by adding 7 to both sides of the equation. Next, subtract 1/2x from both sides. This will leave you with a quadratic equation. Finally, solve the quadratic equation using factoring, completing the square, or the quadratic formula.
Let's solve it by factoring. Move all the terms to one side to set the equation to zero: x^2 - (1/2)x - 8 = 0. Factor the equation: (x - 4)(x + 2) = 0. Set each factor equal to zero and solve: x - 4 = 0 or x + 2 = 0. Solving for x gives us x = 4 or x = -2. Therefore, the solutions to the equation are x = 4 and x = -2.
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