7x^2+42x+45=

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Solution for 7x^2+42x+45= equation:


Simplifying
7x2 + 42x + 45 = 0

Reorder the terms:
45 + 42x + 7x2 = 0

Solving
45 + 42x + 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 + 6x + x2 = 0

Move the constant term to the right:

Add '-6.428571429' to each side of the equation.
6.428571429 + 6x + -6.428571429 + x2 = 0 + -6.428571429

Reorder the terms:
6.428571429 + -6.428571429 + 6x + x2 = 0 + -6.428571429

Combine like terms: 6.428571429 + -6.428571429 = 0.000000000
0.000000000 + 6x + x2 = 0 + -6.428571429
6x + x2 = 0 + -6.428571429

Combine like terms: 0 + -6.428571429 = -6.428571429
6x + x2 = -6.428571429

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = -6.428571429 + 9

Reorder the terms:
9 + 6x + x2 = -6.428571429 + 9

Combine like terms: -6.428571429 + 9 = 2.571428571
9 + 6x + x2 = 2.571428571

Factor a perfect square on the left side:
(x + 3)(x + 3) = 2.571428571

Calculate the square root of the right side: 1.603567451

Break this problem into two subproblems by setting 
(x + 3) equal to 1.603567451 and -1.603567451.

Subproblem 1

x + 3 = 1.603567451 Simplifying x + 3 = 1.603567451 Reorder the terms: 3 + x = 1.603567451 Solving 3 + x = 1.603567451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 1.603567451 + -3 Combine like terms: 3 + -3 = 0 0 + x = 1.603567451 + -3 x = 1.603567451 + -3 Combine like terms: 1.603567451 + -3 = -1.396432549 x = -1.396432549 Simplifying x = -1.396432549

Subproblem 2

x + 3 = -1.603567451 Simplifying x + 3 = -1.603567451 Reorder the terms: 3 + x = -1.603567451 Solving 3 + x = -1.603567451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -1.603567451 + -3 Combine like terms: 3 + -3 = 0 0 + x = -1.603567451 + -3 x = -1.603567451 + -3 Combine like terms: -1.603567451 + -3 = -4.603567451 x = -4.603567451 Simplifying x = -4.603567451

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-1.396432549, -4.603567451}

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