How do you complete the square to solve #0=5x^2 + 2x - 3#?

Answer 1

#x = 3/5# or #x = -1#

Put your equation in standard form in step 1.

#5x^2 + 2x -3 = 0#

Step 2: Shift the constant to the equation's right side.

Add #3# to each side .
#5x^2+2x -3 +3 = 0+3#
#5x^2+2x = 3#
Step 3. Divide both sides of the equation by the coefficient of #x^2#.

Each of the two sides is divided by 5.

#x^2 +2/5x =3/5#

Step 4: Divide by 4 after squareing the coefficient of x.

#(2/5)^2/4 = (4/25)/4 = 1/25#

Step 5: Increase the outcome on both sides.

#x^2 +2/5x + 1/25 =3/5 + 1/25#
#x^2 +2/5x + 1/25= 15/25 + 1/25#
#x^2 +2/5x + 1/25 =16/25#

Step 6: Calculate each side's square root.

#x+1/5 = ±4/5 #

Case 1

#x_1 + 1/5 = +4/5#
#x_1 = 4/5-1/5 = (4-1)/5#
#x_1 = 3/5#

Case 2

#x_2 + 1/5 = -4/5#
#x_2 = -4/5-1/5 = (-4-1)/5 = (-5)/5#
#x_2 = -1#
So #x = 3/5# or #x = -1#
Check: Substitute the values of #x# back into the quadratic.
(a) #x = 3/5#
#5x^2 + 2x -3 = 5(3/5)^2 + 2(3/5) -3 = 5(9/25) + 6/5 -3 = 9/5 +6/5 -15/5 = (9+6-15)/5 = 0#.
(b) #x = -1#
#5x^2 + 2x -3 = 5(-1)^2 + 2(-1) -3 = 5(1) – 2 -3 = 5-2-3 = 0#
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Answer 2

To solve the quadratic equation 0 = 5x^2 + 2x - 3 by completing the square, follow these steps:

  1. Move the constant term to the other side of the equation: 5x^2 + 2x = 3

  2. Divide the coefficient of the x^2 term by 2, square the result, and add it to both sides of the equation: 5x^2 + 2x + (2/2)^2 = 3 + (2/2)^2 5x^2 + 2x + 1 = 3 + 1

  3. Factor the left side of the equation as a perfect square: (sqrt(5)x + 1)^2 = 4

  4. Take the square root of both sides to solve for x: sqrt((sqrt(5)x + 1)^2) = ±sqrt(4) sqrt(5)x + 1 = ±2

  5. Subtract 1 from both sides: sqrt(5)x = -1 ± 2

  6. Solve for x: x = (-1 ± 2)/sqrt(5)

Therefore, the solutions to the equation 0 = 5x^2 + 2x - 3 by completing the square are: x = (-1 + 2)/sqrt(5) or x = (-1 - 2)/sqrt(5)

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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.

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.

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.

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.

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