Solve Using the Quadratic Formula 16x^2=56x-49

$16 x^{2} = 56 x - 49$

Step 1

Move all the expressions to the left side of the equation.

Subtract $56 x$ from both sides of the equation.

$16 x^{2} - 56 x = - 49$

Add $49$ to both sides of the equation.

$16 x^{2} - 56 x + 49 = 0$

Step 2

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 3

Substitute the values $a = 16$ , $b = - 56$ , and $c = 49$ into the quadratic formula and solve for $x$ .

$\frac{56 \pm \sqrt{{(- 56)}^{2} - 4 \cdot (16 \cdot 49)}}{2 \cdot 16}$

Step 4

Simplify.

Simplify the numerator.

Raise $- 56$ to the power of $2$ .

$x = \frac{56 \pm \sqrt{3136 - 4 \cdot 16 \cdot 49}}{2 \cdot 16}$

Multiply $- 4 \cdot 16 \cdot 49$ .

Multiply $- 4$ by $16$ .

$x = \frac{56 \pm \sqrt{3136 - 64 \cdot 49}}{2 \cdot 16}$

Multiply $- 64$ by $49$ .

$x = \frac{56 \pm \sqrt{3136 - 3136}}{2 \cdot 16}$

Subtract $3136$ from $3136$ .

$x = \frac{56 \pm \sqrt{0}}{2 \cdot 16}$

Rewrite $0$ as $0^{2}$ .

$x = \frac{56 \pm \sqrt{0^{2}}}{2 \cdot 16}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \frac{56 \pm 0}{2 \cdot 16}$

$56$ plus or minus $0$ is $56$ .

$x = \frac{56}{2 \cdot 16}$

Multiply $2$ by $16$ .

$x = \frac{56}{32}$

Cancel the common factor of $56$ and $32$ .

Factor $8$ out of $56$ .

$x = \frac{8 (7)}{32}$

Cancel the common factors.

Factor $8$ out of $32$ .

$x = \frac{8 \cdot 7}{8 \cdot 4}$

Cancel the common factor.

$x = \frac{8 \cdot 7}{8 \cdot 4}$

Rewrite the expression.

$x = \frac{7}{4}$

Step 5

The final answer is the combination of both solutions.

$x = \frac{7}{4}$ Double roots

Solve Using the Quadratic Formula 16x^2=56x-49

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