Home > Algebra > Completing the Square

How do you complete the square to solve # 2x^2 + 6x =5#?

Answer 1

Abigail Allen

#2x^2+6x = 5#

Extract the common constant factor on the left side #2(x^2+3x) = 5#

Complete the square #2(x^2+3x+(3/2)^2) = 5 + 9/2#

Re-write as a square equal to a constant #(x+3/2)^2 = 19/4#

Take the square root of both sides #x+3/2 = +-sqrt(19)/2#

Isolate #x# for the final solution #x = (-3+-sqrt(19))/2#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Avery Alexander

To complete the square to solve the equation 2x^2 + 6x = 5, first, move the constant term to the other side of the equation: 2x^2 + 6x - 5 = 0. Then, divide every term by the coefficient of x^2, which is 2: x^2 + 3x - 5/2 = 0. Next, take half of the coefficient of x, square it, and add it to both sides of the equation to complete the square: x^2 + 3x + (3/2)^2 - (3/2)^2 - 5/2 = 0. This simplifies to (x + 3/2)^2 - 9/4 - 5/2 = 0. Finally, simplify the constants: (x + 3/2)^2 - 9/4 - 10/4 = 0, which becomes (x + 3/2)^2 - 19/4 = 0.

By signing up, you agree to our Terms of Service and Privacy Policy

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.