Respuesta :
Answer:The solutions are
[0.5, - 7.5]
Step-by-step explanation:
The given quadratic equation is expressed as
x² + 7x - 4 = 0
The given quadratic equation is already in the standard form of
ax² + bx + c
The general formula for solving quadratic equations is expressed as
x = [- b ± √(b² - 4ac)]/2a
From the equation given,
a = 1
b = 7
c = - 4
Therefore,
x = [- 7 ± √(7² - 4 × 1 × - 4)]/2 × 1
x = [- 7 ± √(49 - - 16)]/2
x = [- 7 ± √65]/2
x = (- 7 + √65)/2 or x = (- 7 - √65)/2
x = (- 7 + 8.06)/2 or x = (- 7 - 8.06)/2
x = 0.5 or x = - 7.5
The values of x are either 0.53 or -7.53.
Data;
- a = 1
- b = 7
- c = -4
Quadratic Formula
To solve this problem, we have to use the quadratic formula on this
[tex]y = \frac{-b +- \sqrt{b^2 - 4ac} }{2a}[/tex]
We should substitute the values and solve for the solutions
[tex]y = \frac{-b +- \sqrt{b^2 - 4ac} }{2a}\\y = \frac{-7+- \sqrt{7^2 - 4(1*-4)} }{2*1}\\ y = \frac{-7 +- \sqrt{49 + 16} }{2*1} \\y = \frac{-7+-\sqrt{65} }{2} \\y = \frac{-7+- 8.06}{2} \\y = \frac{-7+8.06}{2} = y = \frac{1.06}{2} = 0.53\\\\or\\y = \frac{-7-8.06}{2}= \frac{-15.06}{2} = -7.53[/tex]
From the above calculation, the values of x are either 0.53 or -7.53.
Learn more on quadratic formula here;
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