(4x^2+9x+2)+(5x^2+8x-7)=

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Solution for (4x^2+9x+2)+(5x^2+8x-7)= equation:


Simplifying
(4x2 + 9x + 2) + (5x2 + 8x + -7) = 0

Reorder the terms:
(2 + 9x + 4x2) + (5x2 + 8x + -7) = 0

Remove parenthesis around (2 + 9x + 4x2)
2 + 9x + 4x2 + (5x2 + 8x + -7) = 0

Reorder the terms:
2 + 9x + 4x2 + (-7 + 8x + 5x2) = 0

Remove parenthesis around (-7 + 8x + 5x2)
2 + 9x + 4x2 + -7 + 8x + 5x2 = 0

Reorder the terms:
2 + -7 + 9x + 8x + 4x2 + 5x2 = 0

Combine like terms: 2 + -7 = -5
-5 + 9x + 8x + 4x2 + 5x2 = 0

Combine like terms: 9x + 8x = 17x
-5 + 17x + 4x2 + 5x2 = 0

Combine like terms: 4x2 + 5x2 = 9x2
-5 + 17x + 9x2 = 0

Solving
-5 + 17x + 9x2 = 0

Solving for variable 'x'.

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

Divide each side by '9'.
-0.5555555556 + 1.888888889x + x2 = 0

Move the constant term to the right:

Add '0.5555555556' to each side of the equation.
-0.5555555556 + 1.888888889x + 0.5555555556 + x2 = 0 + 0.5555555556

Reorder the terms:
-0.5555555556 + 0.5555555556 + 1.888888889x + x2 = 0 + 0.5555555556

Combine like terms: -0.5555555556 + 0.5555555556 = 0.0000000000
0.0000000000 + 1.888888889x + x2 = 0 + 0.5555555556
1.888888889x + x2 = 0 + 0.5555555556

Combine like terms: 0 + 0.5555555556 = 0.5555555556
1.888888889x + x2 = 0.5555555556

The x term is 1.888888889x.  Take half its coefficient (0.9444444445).
Square it (0.8919753087) and add it to both sides.

Add '0.8919753087' to each side of the equation.
1.888888889x + 0.8919753087 + x2 = 0.5555555556 + 0.8919753087

Reorder the terms:
0.8919753087 + 1.888888889x + x2 = 0.5555555556 + 0.8919753087

Combine like terms: 0.5555555556 + 0.8919753087 = 1.4475308643
0.8919753087 + 1.888888889x + x2 = 1.4475308643

Factor a perfect square on the left side:
(x + 0.9444444445)(x + 0.9444444445) = 1.4475308643

Calculate the square root of the right side: 1.203133768

Break this problem into two subproblems by setting 
(x + 0.9444444445) equal to 1.203133768 and -1.203133768.

Subproblem 1

x + 0.9444444445 = 1.203133768 Simplifying x + 0.9444444445 = 1.203133768 Reorder the terms: 0.9444444445 + x = 1.203133768 Solving 0.9444444445 + x = 1.203133768 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9444444445' to each side of the equation. 0.9444444445 + -0.9444444445 + x = 1.203133768 + -0.9444444445 Combine like terms: 0.9444444445 + -0.9444444445 = 0.0000000000 0.0000000000 + x = 1.203133768 + -0.9444444445 x = 1.203133768 + -0.9444444445 Combine like terms: 1.203133768 + -0.9444444445 = 0.2586893235 x = 0.2586893235 Simplifying x = 0.2586893235

Subproblem 2

x + 0.9444444445 = -1.203133768 Simplifying x + 0.9444444445 = -1.203133768 Reorder the terms: 0.9444444445 + x = -1.203133768 Solving 0.9444444445 + x = -1.203133768 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9444444445' to each side of the equation. 0.9444444445 + -0.9444444445 + x = -1.203133768 + -0.9444444445 Combine like terms: 0.9444444445 + -0.9444444445 = 0.0000000000 0.0000000000 + x = -1.203133768 + -0.9444444445 x = -1.203133768 + -0.9444444445 Combine like terms: -1.203133768 + -0.9444444445 = -2.1475782125 x = -2.1475782125 Simplifying x = -2.1475782125

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.2586893235, -2.1475782125}

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