Solve k^2344-8-7 - ScanMath

Question

k^{2} \times 344 - 8 - 7

Simplify the expression

344 k^{2} - 15

Evaluate

k^{2} \times 344 - 8 - 7

Use the commutative property to reorder the terms

344 k^{2} - 8 - 7

Solution

344 k^{2} - 15

Show Solution

k_{1} = - \frac{1290}{172}, k_{2} = \frac{1290}{172}

Alternative Form

k_{1} \approx - 0.208817, k_{2} \approx 0.208817

Evaluate

k^{2} \times 344 - 8 - 7

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

k^{2} \times 344 - 8 - 7 = 0

Use the commutative property to reorder the terms

344 k^{2} - 8 - 7 = 0

Subtract the numbers

344 k^{2} - 15 = 0

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

344 k^{2} = 0 + 15

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

344 k^{2} = 15

Divide both sides

\frac{344 k ^{2}}{344} = \frac{15}{344}

Divide the numbers

k^{2} = \frac{15}{344}

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

k = \pm \frac{15}{344}

Simplify the expression

More Steps

Evaluate

\frac{15}{344}

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

\frac{15}{344}

Simplify the radical expression

More Steps

Evaluate

344

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

4 \times 86

Write the number in exponential form with the base of 2

2^{2} \times 86

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

2^{2} \times 86

Reduce the index of the radical and exponent with 2

286

\frac{15}{2 86}

Multiply by the Conjugate

\frac{15 \times 86}{2 86 \times 86}

Multiply the numbers

More Steps

Evaluate

15 \times 86

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

15 \times 86

Calculate the product

1290

\frac{1290}{2 86 \times 86}

Multiply the numbers

More Steps

Evaluate

286 \times 86

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

2 \times 86

Multiply the terms

172

\frac{1290}{172}

k = \pm \frac{1290}{172}

Separate the equation into 2 possible cases

k = \frac{1290}{172} k = - \frac{1290}{172}

Solution

k_{1} = - \frac{1290}{172}, k_{2} = \frac{1290}{172}

Alternative Form

k_{1} \approx - 0.208817, k_{2} \approx 0.208817

Show Solution