0=-4x^2+7x+4

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Solution for 0=-4x^2+7x+4 equation:


Simplifying
0 = -4x2 + 7x + 4

Reorder the terms:
0 = 4 + 7x + -4x2

Solving
0 = 4 + 7x + -4x2

Solving for variable 'x'.

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

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

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

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

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

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

Divide each side by '4'.
-1 + -1.75x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -1.75x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -1.75x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -1.75x + x2 = 0 + 1
-1.75x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-1.75x + x2 = 1

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 = 1 + 0.765625

Reorder the terms:
0.765625 + -1.75x + x2 = 1 + 0.765625

Combine like terms: 1 + 0.765625 = 1.765625
0.765625 + -1.75x + x2 = 1.765625

Factor a perfect square on the left side:
(x + -0.875)(x + -0.875) = 1.765625

Calculate the square root of the right side: 1.328768227

Break this problem into two subproblems by setting 
(x + -0.875) equal to 1.328768227 and -1.328768227.

Subproblem 1

x + -0.875 = 1.328768227 Simplifying x + -0.875 = 1.328768227 Reorder the terms: -0.875 + x = 1.328768227 Solving -0.875 + x = 1.328768227 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 = 1.328768227 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + x = 1.328768227 + 0.875 x = 1.328768227 + 0.875 Combine like terms: 1.328768227 + 0.875 = 2.203768227 x = 2.203768227 Simplifying x = 2.203768227

Subproblem 2

x + -0.875 = -1.328768227 Simplifying x + -0.875 = -1.328768227 Reorder the terms: -0.875 + x = -1.328768227 Solving -0.875 + x = -1.328768227 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 = -1.328768227 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + x = -1.328768227 + 0.875 x = -1.328768227 + 0.875 Combine like terms: -1.328768227 + 0.875 = -0.453768227 x = -0.453768227 Simplifying x = -0.453768227

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.203768227, -0.453768227}

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