How do you find the solution to the quadratic equation x2−4x−3=0?

Question

Joy Compton · Accepted Answer

Step 1
There are no whole numbers which multiply to -3 and sum to -4
We can solve using the method of completing the square the coefficient of the

x^{2}

term is 1
add subtract

{(\frac{1}{2} coefficient of the x-term)}^{2}

to

x^{2} - 4 x

\Rightarrow x^{2} + 2 (- 2) x + 4 - 4 - 3 = 0

\Rightarrow {(x - 2)}^{2} - 7 = 0

\Rightarrow {(x - 2)}^{2} = 7

take the square root of both sides

\Rightarrow x - 2 = \pm \sqrt{7} \leftarrow

note plus or minus

\Rightarrow x = 2 \pm \sqrt{7} \leftarrow

exact solutions

coolbananas03ok · Accepted Answer

Step 1
Apply quadratic formula for this equation instead of factor it out.
1)

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

2)

(\frac{- (- 4) \pm \sqrt{{(- 4)}^{2} - 4 (1) (- 3)}}{2 (1)})

3)

(\frac{4 \pm \sqrt{16 + 12}}{2})

4)

(\frac{4 \pm 2 \sqrt{7}}{2})

(2 cancel out)
5)

x = 2 \pm \sqrt{7}

RizerMix · Accepted Answer

Step 1 Here, ⇒x2−4x+4−7=0 ⇒(x−2)2=7=(7)2 ⇒x−2=±7 ⇒x=2±7 or Comparing with quadratic equation, ax2+bx+c=0⇒a=1, b=−4, c=−3 △=b2−4ac=(−4)2−4(1)(−3) ⇒△=16+12=28=4×7 △=27 So, x=−b±△2a x=4±272(1) x=2±7

How do you find the solution to the quadratic equation

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