Math

Question Solve the quadratic equation 67t276=0\frac{6}{7} t^{2} - \frac{7}{6} = 0 to find the value of tt.

Studdy Solution

STEP 1

Assumptions
1. We are given the quadratic equation 67t276=0\frac{6}{7} t^{2}-\frac{7}{6}=0.
2. We need to solve for the variable tt.

STEP 2

To solve the equation, we will first isolate the term containing the variable tt on one side of the equation.
67t2=76\frac{6}{7} t^{2} = \frac{7}{6}

STEP 3

Next, we multiply both sides of the equation by the reciprocal of 67\frac{6}{7} to solve for t2t^{2}.
t2=76×76t^{2} = \frac{7}{6} \times \frac{7}{6}

STEP 4

Now, we calculate the right side of the equation.
t2=4936t^{2} = \frac{49}{36}

STEP 5

To find the value of tt, we take the square root of both sides of the equation. Remember that taking the square root of a number yields two solutions: one positive and one negative.
t=±4936t = \pm \sqrt{\frac{49}{36}}

STEP 6

Simplify the square root of the fraction by taking the square root of the numerator and the denominator separately.
t=±4936t = \pm \frac{\sqrt{49}}{\sqrt{36}}

STEP 7

Calculate the square roots.
t=±76t = \pm \frac{7}{6}

STEP 8

Thus, the solutions to the equation are:
t=76andt=76t = \frac{7}{6} \quad \text{and} \quad t = -\frac{7}{6}

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