4x^2+2.4x+0.36=9.7

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Solution for 4x^2+2.4x+0.36=9.7 equation:


Simplifying
4x2 + 2.4x + 0.36 = 9.7

Reorder the terms:
0.36 + 2.4x + 4x2 = 9.7

Solving
0.36 + 2.4x + 4x2 = 9.7

Solving for variable 'x'.

Reorder the terms:
0.36 + -9.7 + 2.4x + 4x2 = 9.7 + -9.7

Combine like terms: 0.36 + -9.7 = -9.34
-9.34 + 2.4x + 4x2 = 9.7 + -9.7

Combine like terms: 9.7 + -9.7 = 0.0
-9.34 + 2.4x + 4x2 = 0.0

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

Divide each side by '4'.
-2.335 + 0.6x + x2 = 0.0

Move the constant term to the right:

Add '2.335' to each side of the equation.
-2.335 + 0.6x + 2.335 + x2 = 0.0 + 2.335

Reorder the terms:
-2.335 + 2.335 + 0.6x + x2 = 0.0 + 2.335

Combine like terms: -2.335 + 2.335 = 0.000
0.000 + 0.6x + x2 = 0.0 + 2.335
0.6x + x2 = 0.0 + 2.335

Combine like terms: 0.0 + 2.335 = 2.335
0.6x + x2 = 2.335

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 = 2.335 + 0.09

Reorder the terms:
0.09 + 0.6x + x2 = 2.335 + 0.09

Combine like terms: 2.335 + 0.09 = 2.425
0.09 + 0.6x + x2 = 2.425

Factor a perfect square on the left side:
(x + 0.3)(x + 0.3) = 2.425

Calculate the square root of the right side: 1.55724115

Break this problem into two subproblems by setting 
(x + 0.3) equal to 1.55724115 and -1.55724115.

Subproblem 1

x + 0.3 = 1.55724115 Simplifying x + 0.3 = 1.55724115 Reorder the terms: 0.3 + x = 1.55724115 Solving 0.3 + x = 1.55724115 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 = 1.55724115 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = 1.55724115 + -0.3 x = 1.55724115 + -0.3 Combine like terms: 1.55724115 + -0.3 = 1.25724115 x = 1.25724115 Simplifying x = 1.25724115

Subproblem 2

x + 0.3 = -1.55724115 Simplifying x + 0.3 = -1.55724115 Reorder the terms: 0.3 + x = -1.55724115 Solving 0.3 + x = -1.55724115 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 = -1.55724115 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = -1.55724115 + -0.3 x = -1.55724115 + -0.3 Combine like terms: -1.55724115 + -0.3 = -1.85724115 x = -1.85724115 Simplifying x = -1.85724115

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.25724115, -1.85724115}

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