4x^2+7x=8

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Solution for 4x^2+7x=8 equation:


Simplifying
4x2 + 7x = 8

Reorder the terms:
7x + 4x2 = 8

Solving
7x + 4x2 = 8

Solving for variable 'x'.

Reorder the terms:
-8 + 7x + 4x2 = 8 + -8

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

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

Divide each side by '4'.
-2 + 1.75x + x2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 1.75x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + 1.75x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 1.75x + x2 = 0 + 2
1.75x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
1.75x + x2 = 2

The x term is 1.75x.  Take half its coefficient (0.875).
Square it (0.765625) and add it to both sides.

Add '0.765625' to each side of the equation.
1.75x + 0.765625 + x2 = 2 + 0.765625

Reorder the terms:
0.765625 + 1.75x + x2 = 2 + 0.765625

Combine like terms: 2 + 0.765625 = 2.765625
0.765625 + 1.75x + x2 = 2.765625

Factor a perfect square on the left side:
(x + 0.875)(x + 0.875) = 2.765625

Calculate the square root of the right side: 1.663016837

Break this problem into two subproblems by setting 
(x + 0.875) equal to 1.663016837 and -1.663016837.

Subproblem 1

x + 0.875 = 1.663016837 Simplifying x + 0.875 = 1.663016837 Reorder the terms: 0.875 + x = 1.663016837 Solving 0.875 + x = 1.663016837 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + x = 1.663016837 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = 1.663016837 + -0.875 x = 1.663016837 + -0.875 Combine like terms: 1.663016837 + -0.875 = 0.788016837 x = 0.788016837 Simplifying x = 0.788016837

Subproblem 2

x + 0.875 = -1.663016837 Simplifying x + 0.875 = -1.663016837 Reorder the terms: 0.875 + x = -1.663016837 Solving 0.875 + x = -1.663016837 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + x = -1.663016837 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = -1.663016837 + -0.875 x = -1.663016837 + -0.875 Combine like terms: -1.663016837 + -0.875 = -2.538016837 x = -2.538016837 Simplifying x = -2.538016837

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.788016837, -2.538016837}

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