Question

Find the value of x in 5x + x² =13²

Answer 1

Answer:

5 x + x^2 = (13)^2

5x + x^2 = 169

5*x + x^2 = 169

x + x*x = 169

5

2x^2 = 169.

5

cross multiplication

10 x^2 = 169

10 * x^2 = 169

x^2 = 169/10

x^2 = 16.9

x =√ 16.9

x = 1.3

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Answer 2

The value of x is 10.738 or -15.738

Solution:

Given that,

$5x + x^2 = 13^2\\\\Simplify\\\\5x + x^2 = 169\\\\x^2 + 5x - 169 = 0$

Solve by quadratic formula

$\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}$

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

$\mathrm{For\:}\quad a=1,\:b=5,\:c=-169\\\\\quad x=\frac{-5\pm \sqrt{5^2-4\cdot \:1\left(-169\right)}}{2\cdot \:1}$

$x = \frac{-5 \pm \sqrt{25 + 676}}{2}\\\\x = \frac{-5 \pm \sqrt{701}}{2}$

$x = \frac{-5 \pm 26.476}{2}$

$We\ have\ two\ solutions$

$x = \frac{-5 + 26.476}{2}\\\\x = \frac{21.476}{2}\\\\x = 10.738$

$Another\ solution\ is:$

$x = \frac{-5 - 26.476}{2}\\\\x = \frac{-31.476}{2}\\\\x = -15.738$

Thus value of x is 10.738 or -15.738

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