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How do you solve #2x^2-1=7x# using the quadratic formula?

Answer 1

Eli Assouline

To solve the equation 2x^2 - 1 = 7x using the quadratic formula, follow these steps:

Identify the coefficients: a = 2, b = -7, and c = -1.
Substitute the values into the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a).
Calculate the discriminant, Δ = b^2 - 4ac.
Substitute the values of a, b, and c into the quadratic formula.
Solve for x using the formula x = (-b ± √Δ) / (2a).
Simplify the expression to find the values of x.

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Answer 2

Isaiah Anthony

#x=(7-sqrt57)/4# and#xx=(7+sqrt57)/4#

#2x^2-1=7x# #=>2x^2-7x-1=0# Dividing bothsides by 2 #=>x^2-7/2x-1/2=0# #=>x^2-2*x*7/4+ (7/4)^2-(7/4)^2-1/2=0# #=> (x-7/4)^2-49/16-1/2=0# #=> (x-7/4)^2-(49+8)/16=0# #=> (x-7/4)^2-(57)/16=0# #=> (x-7/4+(sqrt57)/4)(x-7/4-(sqrt57)/4)=0# #:.# #(x=7/4-sqrt57/4)=>x=(7-sqrt57)/4#

AND #(x=7/4+sqrt57/4)=>x=(7+sqrt57)/4#

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.