-16x^2+90x+7=0

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Solution for -16x^2+90x+7=0 equation:


Simplifying
-16x2 + 90x + 7 = 0

Reorder the terms:
7 + 90x + -16x2 = 0

Solving
7 + 90x + -16x2 = 0

Solving for variable 'x'.

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

Divide each side by '-16'.
-0.4375 + -5.625x + x2 = 0

Move the constant term to the right:

Add '0.4375' to each side of the equation.
-0.4375 + -5.625x + 0.4375 + x2 = 0 + 0.4375

Reorder the terms:
-0.4375 + 0.4375 + -5.625x + x2 = 0 + 0.4375

Combine like terms: -0.4375 + 0.4375 = 0.0000
0.0000 + -5.625x + x2 = 0 + 0.4375
-5.625x + x2 = 0 + 0.4375

Combine like terms: 0 + 0.4375 = 0.4375
-5.625x + x2 = 0.4375

The x term is -5.625x.  Take half its coefficient (-2.8125).
Square it (7.91015625) and add it to both sides.

Add '7.91015625' to each side of the equation.
-5.625x + 7.91015625 + x2 = 0.4375 + 7.91015625

Reorder the terms:
7.91015625 + -5.625x + x2 = 0.4375 + 7.91015625

Combine like terms: 0.4375 + 7.91015625 = 8.34765625
7.91015625 + -5.625x + x2 = 8.34765625

Factor a perfect square on the left side:
(x + -2.8125)(x + -2.8125) = 8.34765625

Calculate the square root of the right side: 2.889231083

Break this problem into two subproblems by setting 
(x + -2.8125) equal to 2.889231083 and -2.889231083.

Subproblem 1

x + -2.8125 = 2.889231083 Simplifying x + -2.8125 = 2.889231083 Reorder the terms: -2.8125 + x = 2.889231083 Solving -2.8125 + x = 2.889231083 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.8125' to each side of the equation. -2.8125 + 2.8125 + x = 2.889231083 + 2.8125 Combine like terms: -2.8125 + 2.8125 = 0.0000 0.0000 + x = 2.889231083 + 2.8125 x = 2.889231083 + 2.8125 Combine like terms: 2.889231083 + 2.8125 = 5.701731083 x = 5.701731083 Simplifying x = 5.701731083

Subproblem 2

x + -2.8125 = -2.889231083 Simplifying x + -2.8125 = -2.889231083 Reorder the terms: -2.8125 + x = -2.889231083 Solving -2.8125 + x = -2.889231083 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.8125' to each side of the equation. -2.8125 + 2.8125 + x = -2.889231083 + 2.8125 Combine like terms: -2.8125 + 2.8125 = 0.0000 0.0000 + x = -2.889231083 + 2.8125 x = -2.889231083 + 2.8125 Combine like terms: -2.889231083 + 2.8125 = -0.076731083 x = -0.076731083 Simplifying x = -0.076731083

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.701731083, -0.076731083}

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