Math

Question Solve 5u260=05 u^{2}-60=0 for real uu. Round answer to nearest hundredth. If multiple solutions, separate by commas. If no solution, click "No solution".

Studdy Solution

STEP 1

Assumptions
1. We are given the quadratic equation 5u260=05u^2 - 60 = 0.
2. We need to solve for uu where uu is a real number.
3. We will round our answer to the nearest hundredth.

STEP 2

To solve the quadratic equation, we first need to isolate the term containing u2u^2 by moving all other terms to the other side of the equation.
5u2=605u^2 = 60

STEP 3

Next, we divide both sides of the equation by the coefficient of u2u^2 which is 5 to solve for u2u^2.
u2=605u^2 = \frac{60}{5}

STEP 4

Calculate the right-hand side of the equation to find the value of u2u^2.
u2=12u^2 = 12

STEP 5

Now that we have u2=12u^2 = 12, we take the square root of both sides of the equation to solve for uu. Remember that taking the square root of a number yields both a positive and negative solution.
u=±12u = \pm\sqrt{12}

STEP 6

Simplify the square root of 12. Since 12=4×312 = 4 \times 3 and 44 is a perfect square, we can simplify 12\sqrt{12} to 232\sqrt{3}.
u=±23u = \pm2\sqrt{3}

STEP 7

Now we need to approximate the value of 3\sqrt{3} to the nearest hundredth. The value of 3\sqrt{3} is approximately 1.731.73 when rounded to the nearest hundredth.

STEP 8

Multiply 22 by the approximate value of 3\sqrt{3} to find the approximate values of uu.
u±2×1.73u \approx \pm2 \times 1.73

STEP 9

Calculate the approximate values of uu.
u±3.46u \approx \pm3.46

STEP 10

Thus, the solutions to the equation 5u260=05u^2 - 60 = 0 rounded to the nearest hundredth are u3.46u \approx 3.46 and u3.46u \approx -3.46.
The solutions are 3.46,3.463.46, -3.46.

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