7x^2+3x-45=0

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Solution for 7x^2+3x-45=0 equation:


Simplifying
7x2 + 3x + -45 = 0

Reorder the terms:
-45 + 3x + 7x2 = 0

Solving
-45 + 3x + 7x2 = 0

Solving for variable 'x'.

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

Divide each side by '7'.
-6.428571429 + 0.4285714286x + x2 = 0

Move the constant term to the right:

Add '6.428571429' to each side of the equation.
-6.428571429 + 0.4285714286x + 6.428571429 + x2 = 0 + 6.428571429

Reorder the terms:
-6.428571429 + 6.428571429 + 0.4285714286x + x2 = 0 + 6.428571429

Combine like terms: -6.428571429 + 6.428571429 = 0.000000000
0.000000000 + 0.4285714286x + x2 = 0 + 6.428571429
0.4285714286x + x2 = 0 + 6.428571429

Combine like terms: 0 + 6.428571429 = 6.428571429
0.4285714286x + x2 = 6.428571429

The x term is 0.4285714286x.  Take half its coefficient (0.2142857143).
Square it (0.04591836735) and add it to both sides.

Add '0.04591836735' to each side of the equation.
0.4285714286x + 0.04591836735 + x2 = 6.428571429 + 0.04591836735

Reorder the terms:
0.04591836735 + 0.4285714286x + x2 = 6.428571429 + 0.04591836735

Combine like terms: 6.428571429 + 0.04591836735 = 6.47448979635
0.04591836735 + 0.4285714286x + x2 = 6.47448979635

Factor a perfect square on the left side:
(x + 0.2142857143)(x + 0.2142857143) = 6.47448979635

Calculate the square root of the right side: 2.544501876

Break this problem into two subproblems by setting 
(x + 0.2142857143) equal to 2.544501876 and -2.544501876.

Subproblem 1

x + 0.2142857143 = 2.544501876 Simplifying x + 0.2142857143 = 2.544501876 Reorder the terms: 0.2142857143 + x = 2.544501876 Solving 0.2142857143 + x = 2.544501876 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2142857143' to each side of the equation. 0.2142857143 + -0.2142857143 + x = 2.544501876 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + x = 2.544501876 + -0.2142857143 x = 2.544501876 + -0.2142857143 Combine like terms: 2.544501876 + -0.2142857143 = 2.3302161617 x = 2.3302161617 Simplifying x = 2.3302161617

Subproblem 2

x + 0.2142857143 = -2.544501876 Simplifying x + 0.2142857143 = -2.544501876 Reorder the terms: 0.2142857143 + x = -2.544501876 Solving 0.2142857143 + x = -2.544501876 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2142857143' to each side of the equation. 0.2142857143 + -0.2142857143 + x = -2.544501876 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + x = -2.544501876 + -0.2142857143 x = -2.544501876 + -0.2142857143 Combine like terms: -2.544501876 + -0.2142857143 = -2.7587875903 x = -2.7587875903 Simplifying x = -2.7587875903

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.3302161617, -2.7587875903}

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