Solved on Feb 22, 2024

Find the values of y that satisfy the equation 2=4y26y-2=4y^2-6y. Round the solutions to the nearest hundredth.

STEP 1

Assumptions
1. We are given the quadratic equation 2=4y26y-2 = 4y^2 - 6y.
2. We need to solve for yy.
3. The solutions should be in the form of integers or fractions rounded to the nearest hundredth if necessary.

STEP 2

To solve the quadratic equation, we first need to set it to standard form, which is ax2+bx+c=0ax^2 + bx + c = 0. To do this, we will move all terms to one side of the equation.
4y26y+2=04y^2 - 6y + 2 = 0

STEP 3

Now that we have the standard form of the quadratic equation, we can use the quadratic formula to find the values of yy. The quadratic formula is given by:
y=b±b24ac2ay = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

STEP 4

Identify the coefficients aa, bb, and cc from the standard form of the quadratic equation.
a=4,b=6,c=2a = 4, \quad b = -6, \quad c = 2

STEP 5

Substitute the values of aa, bb, and cc into the quadratic formula.
y=(6)±(6)24(4)(2)2(4)y = \frac{-(-6) \pm \sqrt{(-6)^2 - 4(4)(2)}}{2(4)}

STEP 6

Simplify the terms inside the quadratic formula.
y=6±36328y = \frac{6 \pm \sqrt{36 - 32}}{8}

STEP 7

Continue simplifying under the square root.
y=6±48y = \frac{6 \pm \sqrt{4}}{8}

STEP 8

Take the square root of 4.
y=6±28y = \frac{6 \pm 2}{8}

STEP 9

Now, we have two possible solutions for yy, which come from the plus and minus in the quadratic formula. Let's solve for each one.
First, using the plus sign:
y=6+28y = \frac{6 + 2}{8}

STEP 10

Calculate the value for the first solution.
y=88y = \frac{8}{8}

STEP 11

Simplify the fraction.
y=1y = 1

STEP 12

Now, using the minus sign:
y=628y = \frac{6 - 2}{8}

STEP 13

Calculate the value for the second solution.
y=48y = \frac{4}{8}

STEP 14

Simplify the fraction.
y=12y = \frac{1}{2}
The solutions to the quadratic equation are y=1y = 1 or y=12y = \frac{1}{2}.

Was this helpful?
banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ContactInfluencer programPolicyTerms
TwitterInstagramFacebookTikTokDiscord