Solve. 16x2−25=0 x=B⊗

Question

Solve.  16x2−25=0  x=B⊗

Jenny Sheppard · Accepted Answer

Step 1  Given Data:  Equation: 16x2−25=0  First, apply factorization in the given equation then solve for the values of x.  The useful factorization is,  (a2−b2)=(a−b)(a+b)  Step 2  Solve the given equation,  16x2−25=0  (4x)2−(5)2=0  (4x-5)(4x+5)=0  x=54 &amp;amp; x=−54  Thus, the values of x are −54 and 54 (or -1.25 and 1.25).

puhnut1m · Accepted Answer

We will first write the equation in standard form

a x^{2} + b x + c = 0

to identify a,b and c.
Where a is the coefficient of the

x^{2}

term, b is the coefficient of the x term and c is the constant term.
Given equation:

16 x^{2} - 25 = 0

The variable in the equation is x:

x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}

Use a=16, b=0 and c=-25:

x = \frac{- (0) \pm \sqrt{{(0)}^{2} - 4 \cdot 16 \cdot (- 25)}}{2 (16)}

x = \frac{- 0 \pm \sqrt{0 + 1600}}{32}

x = \frac{\pm \sqrt{0 + 1600}}{32}

Use

\sqrt{1600} = 40 : x = \frac{\pm 40}{32}

We know

\frac{a \pm b}{c}

means

\frac{a + b}{c}

or

\frac{a - b}{c} : x = \frac{42}{30}

or

x = - \frac{40}{32}

Simplify:

x = \frac{5}{4}

or

x = - \frac{5}{4}

Hence the roots are

- \frac{5}{4}

and

\frac{5}{4}

Solve. 16x^{2}-25=0 x=\Box

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