Solve t^28-49 - ScanMath

Question

Simplify the expression

8 t^{2} - 49

Evaluate

t^{2} \times 8 - 49

Solution

8 t^{2} - 49

Show Solution

t_{1} = - \frac{7 2}{4}, t_{2} = \frac{7 2}{4}

Alternative Form

t_{1} \approx - 2.474874, t_{2} \approx 2.474874

Evaluate

t^{2} \times 8 - 49

To find the roots of the expression,set the expression equal to 0

t^{2} \times 8 - 49 = 0

Use the commutative property to reorder the terms

8 t^{2} - 49 = 0

Move the constant to the right-hand side and change its sign

8 t^{2} = 0 + 49

Removing 0 doesn't change the value,so remove it from the expression

8 t^{2} = 49

Divide both sides

\frac{8 t ^{2}}{8} = \frac{49}{8}

Divide the numbers

t^{2} = \frac{49}{8}

Take the root of both sides of the equation and remember to use both positive and negative roots

t = \pm \frac{49}{8}

Simplify the expression

More Steps

Evaluate

\frac{49}{8}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{49}{8}

Simplify the radical expression

More Steps

Evaluate

49

Write the number in exponential form with the base of 7

7^{2}

Reduce the index of the radical and exponent with 2

7

\frac{7}{8}

Simplify the radical expression

More Steps

Evaluate

8

Write the expression as a product where the root of one of the factors can be evaluated

4 \times 2

Write the number in exponential form with the base of 2

2^{2} \times 2

The root of a product is equal to the product of the roots of each factor

2^{2} \times 2

Reduce the index of the radical and exponent with 2

22

\frac{7}{2 2}

Multiply by the Conjugate

\frac{7 2}{2 2 \times 2}

Multiply the numbers

More Steps

Evaluate

22 \times 2

When a square root of an expression is multiplied by itself,the result is that expression

2 \times 2

Multiply the numbers

4

\frac{7 2}{4}

t = \pm \frac{7 2}{4}

Separate the equation into 2 possible cases

t = \frac{7 2}{4} t = - \frac{7 2}{4}

Solution

t_{1} = - \frac{7 2}{4}, t_{2} = \frac{7 2}{4}

Alternative Form

t_{1} \approx - 2.474874, t_{2} \approx 2.474874

Show Solution