Solve x2 − 3x = −8.

Asked by maham237 @ 26/12/2020 in Mathematics viewed by 279 People

x equals quantity of 3 plus or minus I square root of 29 all over 2
x equals quantity of 3 plus or minus I square root of 23 all over 2
x equals quantity of negative 3 plus or minus I square root of 29 all over 2
x equals quantity of negative 3 plus or minus I square root of 23 all over 2

Answered by maham237 @ 26/12/2020

we have

$x^{2} -3x=-8$

Complete the square. Remember to balance the equation by adding the same constants to each side

$x^{2} -3x+1.5^{2}=-8+1.5^{2}$

$x^{2} -3x+1.5^{2}=-5.75$

Rewrite as perfect squares

$(x-1.5)^{2}=-5.75$

Square Root both sides

$x-1.5=(+/-)\sqrt{-5.75}$

Remember that

$\sqrt{-1}=i$

$\sqrt{5.75}= \sqrt{\frac{23}{4}}=\frac{\sqrt{23}}{2}$

Substitute

$x-1.5=(+/-)i\frac{\sqrt{23}}{2}$

$x=1.5(+/-)i\frac{\sqrt{23}}{2}$

$x=(3/2)(+/-)i\frac{\sqrt{23}}{2}$

$x=(3/2)+i\frac{\sqrt{23}}{2}=\frac{3+i\sqrt{23}}{2}$

$x=(3/2)-i\frac{\sqrt{23}}{2}=\frac{3-i\sqrt{23}}{2}$

therefore

the answer is

x equals quantity of 3 plus or minus I square root of 23 all over 2

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