-2.9x^2-7.6x+1.9=3.5

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Solution for -2.9x^2-7.6x+1.9=3.5 equation:


Simplifying
-2.9x2 + -7.6x + 1.9 = 3.5

Reorder the terms:
1.9 + -7.6x + -2.9x2 = 3.5

Solving
1.9 + -7.6x + -2.9x2 = 3.5

Solving for variable 'x'.

Reorder the terms:
1.9 + -3.5 + -7.6x + -2.9x2 = 3.5 + -3.5

Combine like terms: 1.9 + -3.5 = -1.6
-1.6 + -7.6x + -2.9x2 = 3.5 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
-1.6 + -7.6x + -2.9x2 = 0.0

Begin completing the square.  Divide all terms by
-2.9 the coefficient of the squared term: 

Divide each side by '-2.9'.
0.5517241379 + 2.620689655x + x2 = 0

Move the constant term to the right:

Add '-0.5517241379' to each side of the equation.
0.5517241379 + 2.620689655x + -0.5517241379 + x2 = 0 + -0.5517241379

Reorder the terms:
0.5517241379 + -0.5517241379 + 2.620689655x + x2 = 0 + -0.5517241379

Combine like terms: 0.5517241379 + -0.5517241379 = 0.0000000000
0.0000000000 + 2.620689655x + x2 = 0 + -0.5517241379
2.620689655x + x2 = 0 + -0.5517241379

Combine like terms: 0 + -0.5517241379 = -0.5517241379
2.620689655x + x2 = -0.5517241379

The x term is 2.620689655x.  Take half its coefficient (1.310344828).
Square it (1.717003568) and add it to both sides.

Add '1.717003568' to each side of the equation.
2.620689655x + 1.717003568 + x2 = -0.5517241379 + 1.717003568

Reorder the terms:
1.717003568 + 2.620689655x + x2 = -0.5517241379 + 1.717003568

Combine like terms: -0.5517241379 + 1.717003568 = 1.1652794301
1.717003568 + 2.620689655x + x2 = 1.1652794301

Factor a perfect square on the left side:
(x + 1.310344828)(x + 1.310344828) = 1.1652794301

Calculate the square root of the right side: 1.079481093

Break this problem into two subproblems by setting 
(x + 1.310344828) equal to 1.079481093 and -1.079481093.

Subproblem 1

x + 1.310344828 = 1.079481093 Simplifying x + 1.310344828 = 1.079481093 Reorder the terms: 1.310344828 + x = 1.079481093 Solving 1.310344828 + x = 1.079481093 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.310344828' to each side of the equation. 1.310344828 + -1.310344828 + x = 1.079481093 + -1.310344828 Combine like terms: 1.310344828 + -1.310344828 = 0.000000000 0.000000000 + x = 1.079481093 + -1.310344828 x = 1.079481093 + -1.310344828 Combine like terms: 1.079481093 + -1.310344828 = -0.230863735 x = -0.230863735 Simplifying x = -0.230863735

Subproblem 2

x + 1.310344828 = -1.079481093 Simplifying x + 1.310344828 = -1.079481093 Reorder the terms: 1.310344828 + x = -1.079481093 Solving 1.310344828 + x = -1.079481093 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.310344828' to each side of the equation. 1.310344828 + -1.310344828 + x = -1.079481093 + -1.310344828 Combine like terms: 1.310344828 + -1.310344828 = 0.000000000 0.000000000 + x = -1.079481093 + -1.310344828 x = -1.079481093 + -1.310344828 Combine like terms: -1.079481093 + -1.310344828 = -2.389825921 x = -2.389825921 Simplifying x = -2.389825921

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.230863735, -2.389825921}

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