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Sagot :
Answer:
x = 25 and x = 5
Explanation:
Step 1
b is the number beside the x, so (b/2)^2 is equal to:
[tex](\frac{b}{2})^2=(\frac{-30}{2})^2=(-15)^2=225[/tex]So, if we add 225 to both sides of the equation, we get:
x² - 30x = -125
x² - 30x + 225 = -125 + 225
x² - 30x + 225 = 100
Step 2
Now, we can factor the left side of the equation, the expression x² - 30x + 225 is a perfect square trinomial because the first and third terms are perfect squares and the second term is 2 times the square root of the other terms
[tex]\begin{gathered} \sqrt[]{x^2}=x \\ \sqrt[]{225}=15 \\ -30x=-2(15)(x) \end{gathered}[/tex]Therefore, the factorization will be:
[tex](x-15)^2=100[/tex]Step 3
Then, the square root of both sides is equal to:
[tex]\begin{gathered} \sqrt[]{(x-15)^2}=\sqrt[]{100} \\ x-15=10_{} \\ or \\ x-15=-10 \end{gathered}[/tex]Step 4
Therefore, the solutions of the equation are:
x - 15 = 10
x - 15 + 15 = 10 + 15
x = 25
or
x - 15 = -10
x - 15 + 15 = -10 + 15
x = 5
Therefore, the solution of the equation are:
x = 25 and x = 5
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