4x^2+7x-20=0

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Solution for 4x^2+7x-20=0 equation:


Simplifying
4x2 + 7x + -20 = 0

Reorder the terms:
-20 + 7x + 4x2 = 0

Solving
-20 + 7x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
-5 + 1.75x + x2 = 0

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 1.75x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + 1.75x + x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 1.75x + x2 = 0 + 5
1.75x + x2 = 0 + 5

Combine like terms: 0 + 5 = 5
1.75x + x2 = 5

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 = 5 + 0.765625

Reorder the terms:
0.765625 + 1.75x + x2 = 5 + 0.765625

Combine like terms: 5 + 0.765625 = 5.765625
0.765625 + 1.75x + x2 = 5.765625

Factor a perfect square on the left side:
(x + 0.875)(x + 0.875) = 5.765625

Calculate the square root of the right side: 2.401171589

Break this problem into two subproblems by setting 
(x + 0.875) equal to 2.401171589 and -2.401171589.

Subproblem 1

x + 0.875 = 2.401171589 Simplifying x + 0.875 = 2.401171589 Reorder the terms: 0.875 + x = 2.401171589 Solving 0.875 + x = 2.401171589 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 = 2.401171589 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = 2.401171589 + -0.875 x = 2.401171589 + -0.875 Combine like terms: 2.401171589 + -0.875 = 1.526171589 x = 1.526171589 Simplifying x = 1.526171589

Subproblem 2

x + 0.875 = -2.401171589 Simplifying x + 0.875 = -2.401171589 Reorder the terms: 0.875 + x = -2.401171589 Solving 0.875 + x = -2.401171589 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 = -2.401171589 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = -2.401171589 + -0.875 x = -2.401171589 + -0.875 Combine like terms: -2.401171589 + -0.875 = -3.276171589 x = -3.276171589 Simplifying x = -3.276171589

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.526171589, -3.276171589}

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