-4.0x^2+20x+65=

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Solution for -4.0x^2+20x+65= equation:


Simplifying
-4.0x2 + 20x + 65 = 0

Reorder the terms:
65 + 20x + -4.0x2 = 0

Solving
65 + 20x + -4.0x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-4.0 the coefficient of the squared term: 

Divide each side by '-4.0'.
-16.25 + -5x + x2 = 0

Move the constant term to the right:

Add '16.25' to each side of the equation.
-16.25 + -5x + 16.25 + x2 = 0 + 16.25

Reorder the terms:
-16.25 + 16.25 + -5x + x2 = 0 + 16.25

Combine like terms: -16.25 + 16.25 = 0.00
0.00 + -5x + x2 = 0 + 16.25
-5x + x2 = 0 + 16.25

Combine like terms: 0 + 16.25 = 16.25
-5x + x2 = 16.25

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = 16.25 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 16.25 + 6.25

Combine like terms: 16.25 + 6.25 = 22.5
6.25 + -5x + x2 = 22.5

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 22.5

Calculate the square root of the right side: 4.74341649

Break this problem into two subproblems by setting 
(x + -2.5) equal to 4.74341649 and -4.74341649.

Subproblem 1

x + -2.5 = 4.74341649 Simplifying x + -2.5 = 4.74341649 Reorder the terms: -2.5 + x = 4.74341649 Solving -2.5 + x = 4.74341649 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 4.74341649 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 4.74341649 + 2.5 x = 4.74341649 + 2.5 Combine like terms: 4.74341649 + 2.5 = 7.24341649 x = 7.24341649 Simplifying x = 7.24341649

Subproblem 2

x + -2.5 = -4.74341649 Simplifying x + -2.5 = -4.74341649 Reorder the terms: -2.5 + x = -4.74341649 Solving -2.5 + x = -4.74341649 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -4.74341649 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -4.74341649 + 2.5 x = -4.74341649 + 2.5 Combine like terms: -4.74341649 + 2.5 = -2.24341649 x = -2.24341649 Simplifying x = -2.24341649

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.24341649, -2.24341649}

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