7.4+4.77591194x=4.9x^2

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Solution for 7.4+4.77591194x=4.9x^2 equation:


Simplifying
7.4 + 4.77591194x = 4.9x2

Solving
7.4 + 4.77591194x = 4.9x2

Solving for variable 'x'.

Combine like terms: 4.9x2 + -4.9x2 = 0.0
7.4 + 4.77591194x + -4.9x2 = 0.0

Begin completing the square.  Divide all terms by
-4.9 the coefficient of the squared term: 

Divide each side by '-4.9'.
-1.510204082 + -0.9746759061x + x2 = 0

Move the constant term to the right:

Add '1.510204082' to each side of the equation.
-1.510204082 + -0.9746759061x + 1.510204082 + x2 = 0 + 1.510204082

Reorder the terms:
-1.510204082 + 1.510204082 + -0.9746759061x + x2 = 0 + 1.510204082

Combine like terms: -1.510204082 + 1.510204082 = 0.000000000
0.000000000 + -0.9746759061x + x2 = 0 + 1.510204082
-0.9746759061x + x2 = 0 + 1.510204082

Combine like terms: 0 + 1.510204082 = 1.510204082
-0.9746759061x + x2 = 1.510204082

The x term is -0.9746759061x.  Take half its coefficient (-0.4873379531).
Square it (0.2374982805) and add it to both sides.

Add '0.2374982805' to each side of the equation.
-0.9746759061x + 0.2374982805 + x2 = 1.510204082 + 0.2374982805

Reorder the terms:
0.2374982805 + -0.9746759061x + x2 = 1.510204082 + 0.2374982805

Combine like terms: 1.510204082 + 0.2374982805 = 1.7477023625
0.2374982805 + -0.9746759061x + x2 = 1.7477023625

Factor a perfect square on the left side:
(x + -0.4873379531)(x + -0.4873379531) = 1.7477023625

Calculate the square root of the right side: 1.322006945

Break this problem into two subproblems by setting 
(x + -0.4873379531) equal to 1.322006945 and -1.322006945.

Subproblem 1

x + -0.4873379531 = 1.322006945 Simplifying x + -0.4873379531 = 1.322006945 Reorder the terms: -0.4873379531 + x = 1.322006945 Solving -0.4873379531 + x = 1.322006945 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4873379531' to each side of the equation. -0.4873379531 + 0.4873379531 + x = 1.322006945 + 0.4873379531 Combine like terms: -0.4873379531 + 0.4873379531 = 0.0000000000 0.0000000000 + x = 1.322006945 + 0.4873379531 x = 1.322006945 + 0.4873379531 Combine like terms: 1.322006945 + 0.4873379531 = 1.8093448981 x = 1.8093448981 Simplifying x = 1.8093448981

Subproblem 2

x + -0.4873379531 = -1.322006945 Simplifying x + -0.4873379531 = -1.322006945 Reorder the terms: -0.4873379531 + x = -1.322006945 Solving -0.4873379531 + x = -1.322006945 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4873379531' to each side of the equation. -0.4873379531 + 0.4873379531 + x = -1.322006945 + 0.4873379531 Combine like terms: -0.4873379531 + 0.4873379531 = 0.0000000000 0.0000000000 + x = -1.322006945 + 0.4873379531 x = -1.322006945 + 0.4873379531 Combine like terms: -1.322006945 + 0.4873379531 = -0.8346689919 x = -0.8346689919 Simplifying x = -0.8346689919

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.8093448981, -0.8346689919}

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