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Sole the quadratic equation by completing the square. x^2+10x+15=0Choose the appropriate form and fill in the blanks with the correct numbers. Then solve the equation. If there’s more than one solution, separate them with commas.

Sole The Quadratic Equation By Completing The Square X210x150Choose The Appropriate Form And Fill In The Blanks With The Correct Numbers Then Solve The Equation class=

Sagot :

In the function:

[tex]y=x^2+10x+15[/tex]

the coefficients are:

a = 1

b = 10

c = 15

Then, b/2 = 10/2 = 5. Computing the square of x and b/2, we get:

[tex](x+5)^2=x^2+2\cdot x\cdot5+5^2=x^2+10x+25[/tex]

We can see that the first two terms coincide with the previous function, then we need to add and subtract 25 to that function to complete the square, as follows:

[tex]\begin{gathered} y=x^2+10+15 \\ y=x^2+10+15+25-25 \\ y=(x^2+10+25)+(15-25) \\ y=(x+5)^2-10 \end{gathered}[/tex]

Solving the equation:

[tex]\begin{gathered} (x+5)^2-10=0 \\ (x+5)^2=0+10 \\ (x+5)^2=10 \\ x+5=\sqrt[]{10} \\ This\text{ equation has 2 solutions:} \\ x_1=\sqrt[]{10}-5 \\ Or \\ x_2=-\sqrt[]{10}-5 \end{gathered}[/tex]

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