0=-16x^2+145x+7

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Solution for 0=-16x^2+145x+7 equation:


Simplifying
0 = -16x2 + 145x + 7

Reorder the terms:
0 = 7 + 145x + -16x2

Solving
0 = 7 + 145x + -16x2

Solving for variable 'x'.

Combine like terms: 0 + -7 = -7
-7 + -145x + 16x2 = 7 + 145x + -16x2 + -7 + -145x + 16x2

Reorder the terms:
-7 + -145x + 16x2 = 7 + -7 + 145x + -145x + -16x2 + 16x2

Combine like terms: 7 + -7 = 0
-7 + -145x + 16x2 = 0 + 145x + -145x + -16x2 + 16x2
-7 + -145x + 16x2 = 145x + -145x + -16x2 + 16x2

Combine like terms: 145x + -145x = 0
-7 + -145x + 16x2 = 0 + -16x2 + 16x2
-7 + -145x + 16x2 = -16x2 + 16x2

Combine like terms: -16x2 + 16x2 = 0
-7 + -145x + 16x2 = 0

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

Divide each side by '16'.
-0.4375 + -9.0625x + x2 = 0

Move the constant term to the right:

Add '0.4375' to each side of the equation.
-0.4375 + -9.0625x + 0.4375 + x2 = 0 + 0.4375

Reorder the terms:
-0.4375 + 0.4375 + -9.0625x + x2 = 0 + 0.4375

Combine like terms: -0.4375 + 0.4375 = 0.0000
0.0000 + -9.0625x + x2 = 0 + 0.4375
-9.0625x + x2 = 0 + 0.4375

Combine like terms: 0 + 0.4375 = 0.4375
-9.0625x + x2 = 0.4375

The x term is -9.0625x.  Take half its coefficient (-4.53125).
Square it (20.53222656) and add it to both sides.

Add '20.53222656' to each side of the equation.
-9.0625x + 20.53222656 + x2 = 0.4375 + 20.53222656

Reorder the terms:
20.53222656 + -9.0625x + x2 = 0.4375 + 20.53222656

Combine like terms: 0.4375 + 20.53222656 = 20.96972656
20.53222656 + -9.0625x + x2 = 20.96972656

Factor a perfect square on the left side:
(x + -4.53125)(x + -4.53125) = 20.96972656

Calculate the square root of the right side: 4.579271401

Break this problem into two subproblems by setting 
(x + -4.53125) equal to 4.579271401 and -4.579271401.

Subproblem 1

x + -4.53125 = 4.579271401 Simplifying x + -4.53125 = 4.579271401 Reorder the terms: -4.53125 + x = 4.579271401 Solving -4.53125 + x = 4.579271401 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.53125' to each side of the equation. -4.53125 + 4.53125 + x = 4.579271401 + 4.53125 Combine like terms: -4.53125 + 4.53125 = 0.00000 0.00000 + x = 4.579271401 + 4.53125 x = 4.579271401 + 4.53125 Combine like terms: 4.579271401 + 4.53125 = 9.110521401 x = 9.110521401 Simplifying x = 9.110521401

Subproblem 2

x + -4.53125 = -4.579271401 Simplifying x + -4.53125 = -4.579271401 Reorder the terms: -4.53125 + x = -4.579271401 Solving -4.53125 + x = -4.579271401 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.53125' to each side of the equation. -4.53125 + 4.53125 + x = -4.579271401 + 4.53125 Combine like terms: -4.53125 + 4.53125 = 0.00000 0.00000 + x = -4.579271401 + 4.53125 x = -4.579271401 + 4.53125 Combine like terms: -4.579271401 + 4.53125 = -0.048021401 x = -0.048021401 Simplifying x = -0.048021401

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.110521401, -0.048021401}

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