Solve x^2-12x-7 - ScanMath

Question

Find the roots

x_{1} = 6 - 43, x_{2} = 6 + 43

Alternative Form

x_{1} \approx - 0.557439, x_{2} \approx 12.557439

Evaluate

x^{2} - 12 x - 7

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

x^{2} - 12 x - 7 = 0

Substitute a= 1,b= - 12 and c= - 7 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{12 \pm ( - 12 ) ^{2} - 4 ( - 7 )}{2}

Simplify the expression

More Steps

Evaluate

(- 12)^{2} - 4 (- 7)

Multiply the numbers

More Steps

Evaluate

4 (- 7)

Multiplying or dividing an odd number of negative terms equals a negative

- 4 \times 7

Multiply the numbers

- 28

(- 12)^{2} - (- 28)

Rewrite the expression

1 2^{2} - (- 28)

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

1 2^{2} + 28

Evaluate the power

144 + 28

Add the numbers

172

x = \frac{12 \pm 172}{2}

Simplify the radical expression

More Steps

Evaluate

172

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

4 \times 43

Write the number in exponential form with the base of 2

2^{2} \times 43

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

2^{2} \times 43

Reduce the index of the radical and exponent with 2

243

x = \frac{12 \pm 2 43}{2}

Separate the equation into 2 possible cases

x = \frac{12 + 2 43}{2} x = \frac{12 - 2 43}{2}

Simplify the expression

More Steps

Evaluate

x = \frac{12 + 2 43}{2}

Divide the terms

More Steps

Evaluate

\frac{12 + 2 43}{2}

Rewrite the expression

\frac{2 ( 6 + 43 )}{2}

Reduce the fraction

6 + 43

x = 6 + 43

x = 6 + 43 x = \frac{12 - 2 43}{2}

Simplify the expression

More Steps

Evaluate

x = \frac{12 - 2 43}{2}

Divide the terms

More Steps

Evaluate

\frac{12 - 2 43}{2}

Rewrite the expression

\frac{2 ( 6 - 43 )}{2}

Reduce the fraction

6 - 43

x = 6 - 43

x = 6 + 43 x = 6 - 43

Solution

x_{1} = 6 - 43, x_{2} = 6 + 43

Alternative Form

x_{1} \approx - 0.557439, x_{2} \approx 12.557439

Show Solution