5x^2-13=-9x

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Solution for 5x^2-13=-9x equation:


Simplifying
5x2 + -13 = -9x

Reorder the terms:
-13 + 5x2 = -9x

Solving
-13 + 5x2 = -9x

Solving for variable 'x'.

Reorder the terms:
-13 + 9x + 5x2 = -9x + 9x

Combine like terms: -9x + 9x = 0
-13 + 9x + 5x2 = 0

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

Divide each side by '5'.
-2.6 + 1.8x + x2 = 0

Move the constant term to the right:

Add '2.6' to each side of the equation.
-2.6 + 1.8x + 2.6 + x2 = 0 + 2.6

Reorder the terms:
-2.6 + 2.6 + 1.8x + x2 = 0 + 2.6

Combine like terms: -2.6 + 2.6 = 0.0
0.0 + 1.8x + x2 = 0 + 2.6
1.8x + x2 = 0 + 2.6

Combine like terms: 0 + 2.6 = 2.6
1.8x + x2 = 2.6

The x term is 1.8x.  Take half its coefficient (0.9).
Square it (0.81) and add it to both sides.

Add '0.81' to each side of the equation.
1.8x + 0.81 + x2 = 2.6 + 0.81

Reorder the terms:
0.81 + 1.8x + x2 = 2.6 + 0.81

Combine like terms: 2.6 + 0.81 = 3.41
0.81 + 1.8x + x2 = 3.41

Factor a perfect square on the left side:
(x + 0.9)(x + 0.9) = 3.41

Calculate the square root of the right side: 1.846618531

Break this problem into two subproblems by setting 
(x + 0.9) equal to 1.846618531 and -1.846618531.

Subproblem 1

x + 0.9 = 1.846618531 Simplifying x + 0.9 = 1.846618531 Reorder the terms: 0.9 + x = 1.846618531 Solving 0.9 + x = 1.846618531 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + x = 1.846618531 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = 1.846618531 + -0.9 x = 1.846618531 + -0.9 Combine like terms: 1.846618531 + -0.9 = 0.946618531 x = 0.946618531 Simplifying x = 0.946618531

Subproblem 2

x + 0.9 = -1.846618531 Simplifying x + 0.9 = -1.846618531 Reorder the terms: 0.9 + x = -1.846618531 Solving 0.9 + x = -1.846618531 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + x = -1.846618531 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = -1.846618531 + -0.9 x = -1.846618531 + -0.9 Combine like terms: -1.846618531 + -0.9 = -2.746618531 x = -2.746618531 Simplifying x = -2.746618531

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.946618531, -2.746618531}

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