5x^2-3x=142

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Solution for 5x^2-3x=142 equation:


Simplifying
5x2 + -3x = 142

Reorder the terms:
-3x + 5x2 = 142

Solving
-3x + 5x2 = 142

Solving for variable 'x'.

Reorder the terms:
-142 + -3x + 5x2 = 142 + -142

Combine like terms: 142 + -142 = 0
-142 + -3x + 5x2 = 0

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

Divide each side by '5'.
-28.4 + -0.6x + x2 = 0

Move the constant term to the right:

Add '28.4' to each side of the equation.
-28.4 + -0.6x + 28.4 + x2 = 0 + 28.4

Reorder the terms:
-28.4 + 28.4 + -0.6x + x2 = 0 + 28.4

Combine like terms: -28.4 + 28.4 = 0.0
0.0 + -0.6x + x2 = 0 + 28.4
-0.6x + x2 = 0 + 28.4

Combine like terms: 0 + 28.4 = 28.4
-0.6x + x2 = 28.4

The x term is -0.6x.  Take half its coefficient (-0.3).
Square it (0.09) and add it to both sides.

Add '0.09' to each side of the equation.
-0.6x + 0.09 + x2 = 28.4 + 0.09

Reorder the terms:
0.09 + -0.6x + x2 = 28.4 + 0.09

Combine like terms: 28.4 + 0.09 = 28.49
0.09 + -0.6x + x2 = 28.49

Factor a perfect square on the left side:
(x + -0.3)(x + -0.3) = 28.49

Calculate the square root of the right side: 5.337602458

Break this problem into two subproblems by setting 
(x + -0.3) equal to 5.337602458 and -5.337602458.

Subproblem 1

x + -0.3 = 5.337602458 Simplifying x + -0.3 = 5.337602458 Reorder the terms: -0.3 + x = 5.337602458 Solving -0.3 + x = 5.337602458 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = 5.337602458 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = 5.337602458 + 0.3 x = 5.337602458 + 0.3 Combine like terms: 5.337602458 + 0.3 = 5.637602458 x = 5.637602458 Simplifying x = 5.637602458

Subproblem 2

x + -0.3 = -5.337602458 Simplifying x + -0.3 = -5.337602458 Reorder the terms: -0.3 + x = -5.337602458 Solving -0.3 + x = -5.337602458 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = -5.337602458 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = -5.337602458 + 0.3 x = -5.337602458 + 0.3 Combine like terms: -5.337602458 + 0.3 = -5.037602458 x = -5.037602458 Simplifying x = -5.037602458

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.637602458, -5.037602458}

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