Question

14 fill in the blank 2.5 points solve the equation: 3 - 4x² = -97 { type your answer... } give the solution as an integer if possible, or in radical form. if no solution, write dne. to enter a radical answer like 5√2 type 5sqrt(2). enter your answer with \and\ in between. for example, -3 and 3 or 5sqrt(2) and -5sqrt(2)

Explanation:

Step1: Isolate the \(x^2\) term

Subtract 3 from both sides of the equation \(3 - 4x^2 = -97\):
\(3 - 4x^2 - 3 = -97 - 3\)
Simplify to get: \(-4x^2 = -100\)

Step2: Solve for \(x^2\)

Divide both sides by -4:
\(\frac{-4x^2}{-4} = \frac{-100}{-4}\)
Simplify to get: \(x^2 = 25\)

Step3: Solve for \(x\)

Take the square root of both sides:
\(x = \pm\sqrt{25}\)
Simplify the square root: \(x = \pm 5\)

Answer:

-5 and 5