5x^2=-15x+4

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Solution for 5x^2=-15x+4 equation:


Simplifying
5x2 = -15x + 4

Reorder the terms:
5x2 = 4 + -15x

Solving
5x2 = 4 + -15x

Solving for variable 'x'.

Reorder the terms:
-4 + 15x + 5x2 = 4 + -15x + -4 + 15x

Reorder the terms:
-4 + 15x + 5x2 = 4 + -4 + -15x + 15x

Combine like terms: 4 + -4 = 0
-4 + 15x + 5x2 = 0 + -15x + 15x
-4 + 15x + 5x2 = -15x + 15x

Combine like terms: -15x + 15x = 0
-4 + 15x + 5x2 = 0

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

Divide each side by '5'.
-0.8 + 3x + x2 = 0

Move the constant term to the right:

Add '0.8' to each side of the equation.
-0.8 + 3x + 0.8 + x2 = 0 + 0.8

Reorder the terms:
-0.8 + 0.8 + 3x + x2 = 0 + 0.8

Combine like terms: -0.8 + 0.8 = 0.0
0.0 + 3x + x2 = 0 + 0.8
3x + x2 = 0 + 0.8

Combine like terms: 0 + 0.8 = 0.8
3x + x2 = 0.8

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 0.8 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 0.8 + 2.25

Combine like terms: 0.8 + 2.25 = 3.05
2.25 + 3x + x2 = 3.05

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 3.05

Calculate the square root of the right side: 1.74642492

Break this problem into two subproblems by setting 
(x + 1.5) equal to 1.74642492 and -1.74642492.

Subproblem 1

x + 1.5 = 1.74642492 Simplifying x + 1.5 = 1.74642492 Reorder the terms: 1.5 + x = 1.74642492 Solving 1.5 + x = 1.74642492 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 1.74642492 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 1.74642492 + -1.5 x = 1.74642492 + -1.5 Combine like terms: 1.74642492 + -1.5 = 0.24642492 x = 0.24642492 Simplifying x = 0.24642492

Subproblem 2

x + 1.5 = -1.74642492 Simplifying x + 1.5 = -1.74642492 Reorder the terms: 1.5 + x = -1.74642492 Solving 1.5 + x = -1.74642492 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -1.74642492 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -1.74642492 + -1.5 x = -1.74642492 + -1.5 Combine like terms: -1.74642492 + -1.5 = -3.24642492 x = -3.24642492 Simplifying x = -3.24642492

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.24642492, -3.24642492}

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