Order the steps for solving this equation using the quadratic formula. 4x ^ 2 - 11x - 3 = 0
First Step: Identify a = 4; b = - 11 , c = - 3
x = (11 plus/minus sqrt(169))/8
x = 24/8 and x = - 2/8
x = (11 plus/minus sqrt((- 11) ^ 2 - 4(4)
(- 3)))/(2(4))
x = (11 + 13)/8 and x = (11 - 13)/8 x = (11 plus/minus 13)/8
x = (11 plus/minus sqrt(121 + 48))/8
x = 3 and x = - 1/4
The correct order of steps for solving the equation using the quadratic formula is as follows:
1. Identify the values of a, b, and c in the quadratic equation.
2. Plug the values of a, b, and c into the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a)
3. Simplify the expression inside the square root: b^2 - 4ac.
4. Take the square root of the expression in step 3.
5. Write down the two solutions for x, one with a plus sign and one with a minus sign in front of the square root.
6. Simplify the solutions by dividing the numerical values and combining like terms if necessary.
In this specific example, the correct order of steps would be:
1. Identify a = 4, b = -11, c = -3.
2. Plug the values into the quadratic formula: x = (-(-11) ± √((-11)^2 - 4(4)(-3))) / (2(4)).
3. Simplify the expression inside the square root: (-11)^2 - 4(4)(-3) = 121 + 48 = 169.
4. Take the square root of 169: √169 = 13.
5. Write down the two solutions for x: x = (11 ± 13) / (8).
6. Simplify the solutions: x = (11 + 13) / 8 = 24 / 8 = 3, and x = (11 - 13) / 8 = -2 / 8 = -1/4.
Therefore, the correct order of steps for solving this equation using the quadratic formula is:
1. Identify a = 4, b = -11, c = -3.
2. Plug the values into the quadratic formula: x = (-(-11) ± √((-11)^2 - 4(4)(-3))) / (2(4)).
3. Simplify the expression inside the square root: (-11)^2 - 4(4)(-3) = 121 + 48 = 169.
4. Take the square root of 169: √169 = 13.
5. Write down the two solutions for x: x = (11 ± 13) / (8).
6. Simplify the solutions: x = (11 + 13) / 8 = 24 / 8 = 3, and x = (11 - 13) / 8 = -2 / 8 = -1/4.