Find the smaller solution for 4x2 − 78 = 2
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4x^2 - 78 = 2 ?
if so, then
4x^2 = 80
x^2 = 20
x = ± √20
which of these two solutions is smaller ?
To find the smaller solution for 4x^2 - 78 = 2, we need to solve the equation for x. Here's a step-by-step explanation of how to do it:
Step 1: Start by isolating the x^2 term by subtracting 2 from both sides of the equation:
4x^2 - 78 - 2 = 2 - 2
4x^2 - 80 = 0
Step 2: Divide both sides of the equation by 4 to get rid of the coefficient of x^2:
(4x^2 - 80)/4 = 0/4
x^2 - 20 = 0
Step 3: Bring 20 to the other side of the equation by adding it to both sides:
x^2 - 20 + 20 = 0 + 20
x^2 = 20
Step 4: Find the square root of both sides to solve for x:
√(x^2) = √20
x = ±√20
Step 5: Simplify the square root of 20:
x = ±√(4 x 5)
x = ±2√5
Since we're looking for the smaller solution, we take the negative value of the square root:
x = -2√5
Therefore, the smaller solution for the equation 4x^2 - 78 = 2 is -2√5.