Solve t^2940 - 15 - 74

Question

Simplify the expression

940 t^{2} - 89

Evaluate

t^{2} \times 940 - 15 - 74

Use the commutative property to reorder the terms

940 t^{2} - 15 - 74

Solution

940 t^{2} - 89

Show Solution

t_{1} = - \frac{20915}{470}, t_{2} = \frac{20915}{470}

Alternative Form

t_{1} \approx - 0.307703, t_{2} \approx 0.307703

Evaluate

t^{2} \times 940 - 15 - 74

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

t^{2} \times 940 - 15 - 74 = 0

Use the commutative property to reorder the terms

940 t^{2} - 15 - 74 = 0

Subtract the numbers

940 t^{2} - 89 = 0

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

940 t^{2} = 0 + 89

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

940 t^{2} = 89

Divide both sides

\frac{940 t ^{2}}{940} = \frac{89}{940}

Divide the numbers

t^{2} = \frac{89}{940}

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

t = \pm \frac{89}{940}

Simplify the expression

More Steps

Evaluate

\frac{89}{940}

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

\frac{89}{940}

Simplify the radical expression

More Steps

Evaluate

940

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

4 \times 235

Write the number in exponential form with the base of 2

2^{2} \times 235

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

2^{2} \times 235

Reduce the index of the radical and exponent with 2

2235

\frac{89}{2 235}

Multiply by the Conjugate

\frac{89 \times 235}{2 235 \times 235}

Multiply the numbers

More Steps

Evaluate

89 \times 235

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

89 \times 235

Calculate the product

20915

\frac{20915}{2 235 \times 235}

Multiply the numbers

More Steps

Evaluate

2235 \times 235

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

2 \times 235

Multiply the terms

470

\frac{20915}{470}

t = \pm \frac{20915}{470}

Separate the equation into 2 possible cases

t = \frac{20915}{470} t = - \frac{20915}{470}

Solution

t_{1} = - \frac{20915}{470}, t_{2} = \frac{20915}{470}

Alternative Form

t_{1} \approx - 0.307703, t_{2} \approx 0.307703

Show Solution