Solve by completing the square and hunt for twice the larger root. x^2-9x+3=0

Step-by-step explanation:

Simplifying

x2 + -9x + -3 = 0

Reorder the terms:

-3 + -9x + x2 = 0

Solving

-3 + -9x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.

-3 + -9x + 3 + x2 = 0 + 3

Reorder the terms:

-3 + 3 + -9x + x2 = 0 + 3

Combine like terms: -3 + 3 = 0

0 + -9x + x2 = 0 + 3

-9x + x2 = 0 + 3

Combine like terms: 0 + 3 = 3

-9x + x2 = 3

The x term is -9x.  Take half its coefficient (-4.5).

Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.

-9x + 20.25 + x2 = 3 + 20.25

Reorder the terms:

20.25 + -9x + x2 = 3 + 20.25

Combine like terms: 3 + 20.25 = 23.25

20.25 + -9x + x2 = 23.25

Factor a perfect square on the left side:

(x + -4.5)(x + -4.5) = 23.25

Calculate the square root of the right side: 4.82182538

Break this problem into two subproblems by setting

(x + -4.5) equal to 4.82182538 and -4.82182538.

Subproblem 1

x + -4.5 = 4.82182538

Simplifying

x + -4.5 = 4.82182538

Reorder the terms:

-4.5 + x = 4.82182538

Solving

-4.5 + x = 4.82182538

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '4.5' to each side of the equation.

-4.5 + 4.5 + x = 4.82182538 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0

0.0 + x = 4.82182538 + 4.5

x = 4.82182538 + 4.5

Combine like terms: 4.82182538 + 4.5 = 9.32182538

x = 9.32182538

Simplifying

x = 9.32182538

Subproblem 2

x + -4.5 = -4.82182538

Simplifying

x + -4.5 = -4.82182538

Reorder the terms:

-4.5 + x = -4.82182538

Solving

-4.5 + x = -4.82182538

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '4.5' to each side of the equation.

-4.5 + 4.5 + x = -4.82182538 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0

0.0 + x = -4.82182538 + 4.5

x = -4.82182538 + 4.5

Combine like terms: -4.82182538 + 4.5 = -0.32182538

x = -0.32182538

Simplifying

x = -0.32182538

Solution

The solution to the problem is based on the solutions

from the subproblems.

x = {9.32182538, -0.32182538}

I can anwser the fist part but im not sure what you mean by hunt for twice the larger root. But by completing the square your overall end result by rounding to the hundreths place would be x= (8.65, 0.35)

Step-by-step explanation:

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step-by-step explanation:

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