Solve t^2840-15-63

Question

Simplify the expression

840 t^{2} - 78

Evaluate

t^{2} \times 840 - 15 - 63

Use the commutative property to reorder the terms

840 t^{2} - 15 - 63

Solution

840 t^{2} - 78

Show Solution

6 (140 t^{2} - 13)

Evaluate

t^{2} \times 840 - 15 - 63

Use the commutative property to reorder the terms

840 t^{2} - 15 - 63

Subtract the numbers

840 t^{2} - 78

Solution

6 (140 t^{2} - 13)

Show Solution

t_{1} = - \frac{455}{70}, t_{2} = \frac{455}{70}

Alternative Form

t_{1} \approx - 0.304725, t_{2} \approx 0.304725

Evaluate

t^{2} \times 840 - 15 - 63

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

t^{2} \times 840 - 15 - 63 = 0

Use the commutative property to reorder the terms

840 t^{2} - 15 - 63 = 0

Subtract the numbers

840 t^{2} - 78 = 0

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

840 t^{2} = 0 + 78

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

840 t^{2} = 78

Divide both sides

\frac{840 t ^{2}}{840} = \frac{78}{840}

Divide the numbers

t^{2} = \frac{78}{840}

Cancel out the common factor 6

t^{2} = \frac{13}{140}

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

t = \pm \frac{13}{140}

Simplify the expression

More Steps

Evaluate

\frac{13}{140}

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

\frac{13}{140}

Simplify the radical expression

More Steps

Evaluate

140

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

4 \times 35

Write the number in exponential form with the base of 2

2^{2} \times 35

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

2^{2} \times 35

Reduce the index of the radical and exponent with 2

235

\frac{13}{2 35}

Multiply by the Conjugate

\frac{13 \times 35}{2 35 \times 35}

Multiply the numbers

More Steps

Evaluate

13 \times 35

The product of roots with the same index is equal to the root of the product

13 \times 35

Calculate the product

455

\frac{455}{2 35 \times 35}

Multiply the numbers

More Steps

Evaluate

235 \times 35

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

2 \times 35

Multiply the terms

70

\frac{455}{70}

t = \pm \frac{455}{70}

Separate the equation into 2 possible cases

t = \frac{455}{70} t = - \frac{455}{70}

Solution

t_{1} = - \frac{455}{70}, t_{2} = \frac{455}{70}

Alternative Form

t_{1} \approx - 0.304725, t_{2} \approx 0.304725

Show Solution