0=-8x^2+3x+7

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Solution for 0=-8x^2+3x+7 equation:


Simplifying
0 = -8x2 + 3x + 7

Reorder the terms:
0 = 7 + 3x + -8x2

Solving
0 = 7 + 3x + -8x2

Solving for variable 'x'.

Combine like terms: 0 + -7 = -7
-7 + -3x + 8x2 = 7 + 3x + -8x2 + -7 + -3x + 8x2

Reorder the terms:
-7 + -3x + 8x2 = 7 + -7 + 3x + -3x + -8x2 + 8x2

Combine like terms: 7 + -7 = 0
-7 + -3x + 8x2 = 0 + 3x + -3x + -8x2 + 8x2
-7 + -3x + 8x2 = 3x + -3x + -8x2 + 8x2

Combine like terms: 3x + -3x = 0
-7 + -3x + 8x2 = 0 + -8x2 + 8x2
-7 + -3x + 8x2 = -8x2 + 8x2

Combine like terms: -8x2 + 8x2 = 0
-7 + -3x + 8x2 = 0

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

Divide each side by '8'.
-0.875 + -0.375x + x2 = 0

Move the constant term to the right:

Add '0.875' to each side of the equation.
-0.875 + -0.375x + 0.875 + x2 = 0 + 0.875

Reorder the terms:
-0.875 + 0.875 + -0.375x + x2 = 0 + 0.875

Combine like terms: -0.875 + 0.875 = 0.000
0.000 + -0.375x + x2 = 0 + 0.875
-0.375x + x2 = 0 + 0.875

Combine like terms: 0 + 0.875 = 0.875
-0.375x + x2 = 0.875

The x term is -0.375x.  Take half its coefficient (-0.1875).
Square it (0.03515625) and add it to both sides.

Add '0.03515625' to each side of the equation.
-0.375x + 0.03515625 + x2 = 0.875 + 0.03515625

Reorder the terms:
0.03515625 + -0.375x + x2 = 0.875 + 0.03515625

Combine like terms: 0.875 + 0.03515625 = 0.91015625
0.03515625 + -0.375x + x2 = 0.91015625

Factor a perfect square on the left side:
(x + -0.1875)(x + -0.1875) = 0.91015625

Calculate the square root of the right side: 0.954021095

Break this problem into two subproblems by setting 
(x + -0.1875) equal to 0.954021095 and -0.954021095.

Subproblem 1

x + -0.1875 = 0.954021095 Simplifying x + -0.1875 = 0.954021095 Reorder the terms: -0.1875 + x = 0.954021095 Solving -0.1875 + x = 0.954021095 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1875' to each side of the equation. -0.1875 + 0.1875 + x = 0.954021095 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + x = 0.954021095 + 0.1875 x = 0.954021095 + 0.1875 Combine like terms: 0.954021095 + 0.1875 = 1.141521095 x = 1.141521095 Simplifying x = 1.141521095

Subproblem 2

x + -0.1875 = -0.954021095 Simplifying x + -0.1875 = -0.954021095 Reorder the terms: -0.1875 + x = -0.954021095 Solving -0.1875 + x = -0.954021095 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1875' to each side of the equation. -0.1875 + 0.1875 + x = -0.954021095 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + x = -0.954021095 + 0.1875 x = -0.954021095 + 0.1875 Combine like terms: -0.954021095 + 0.1875 = -0.766521095 x = -0.766521095 Simplifying x = -0.766521095

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.141521095, -0.766521095}

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