10=16x^2+42x+3.75

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Solution for 10=16x^2+42x+3.75 equation:


Simplifying
10 = 16x2 + 42x + 3.75

Reorder the terms:
10 = 3.75 + 42x + 16x2

Solving
10 = 3.75 + 42x + 16x2

Solving for variable 'x'.

Combine like terms: 10 + -3.75 = 6.25
6.25 + -42x + -16x2 = 3.75 + 42x + 16x2 + -3.75 + -42x + -16x2

Reorder the terms:
6.25 + -42x + -16x2 = 3.75 + -3.75 + 42x + -42x + 16x2 + -16x2

Combine like terms: 3.75 + -3.75 = 0.00
6.25 + -42x + -16x2 = 0.00 + 42x + -42x + 16x2 + -16x2
6.25 + -42x + -16x2 = 42x + -42x + 16x2 + -16x2

Combine like terms: 42x + -42x = 0
6.25 + -42x + -16x2 = 0 + 16x2 + -16x2
6.25 + -42x + -16x2 = 16x2 + -16x2

Combine like terms: 16x2 + -16x2 = 0
6.25 + -42x + -16x2 = 0

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

Divide each side by '-16'.
-0.390625 + 2.625x + x2 = 0

Move the constant term to the right:

Add '0.390625' to each side of the equation.
-0.390625 + 2.625x + 0.390625 + x2 = 0 + 0.390625

Reorder the terms:
-0.390625 + 0.390625 + 2.625x + x2 = 0 + 0.390625

Combine like terms: -0.390625 + 0.390625 = 0.000000
0.000000 + 2.625x + x2 = 0 + 0.390625
2.625x + x2 = 0 + 0.390625

Combine like terms: 0 + 0.390625 = 0.390625
2.625x + x2 = 0.390625

The x term is 2.625x.  Take half its coefficient (1.3125).
Square it (1.72265625) and add it to both sides.

Add '1.72265625' to each side of the equation.
2.625x + 1.72265625 + x2 = 0.390625 + 1.72265625

Reorder the terms:
1.72265625 + 2.625x + x2 = 0.390625 + 1.72265625

Combine like terms: 0.390625 + 1.72265625 = 2.11328125
1.72265625 + 2.625x + x2 = 2.11328125

Factor a perfect square on the left side:
(x + 1.3125)(x + 1.3125) = 2.11328125

Calculate the square root of the right side: 1.453712919

Break this problem into two subproblems by setting 
(x + 1.3125) equal to 1.453712919 and -1.453712919.

Subproblem 1

x + 1.3125 = 1.453712919 Simplifying x + 1.3125 = 1.453712919 Reorder the terms: 1.3125 + x = 1.453712919 Solving 1.3125 + x = 1.453712919 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.3125' to each side of the equation. 1.3125 + -1.3125 + x = 1.453712919 + -1.3125 Combine like terms: 1.3125 + -1.3125 = 0.0000 0.0000 + x = 1.453712919 + -1.3125 x = 1.453712919 + -1.3125 Combine like terms: 1.453712919 + -1.3125 = 0.141212919 x = 0.141212919 Simplifying x = 0.141212919

Subproblem 2

x + 1.3125 = -1.453712919 Simplifying x + 1.3125 = -1.453712919 Reorder the terms: 1.3125 + x = -1.453712919 Solving 1.3125 + x = -1.453712919 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.3125' to each side of the equation. 1.3125 + -1.3125 + x = -1.453712919 + -1.3125 Combine like terms: 1.3125 + -1.3125 = 0.0000 0.0000 + x = -1.453712919 + -1.3125 x = -1.453712919 + -1.3125 Combine like terms: -1.453712919 + -1.3125 = -2.766212919 x = -2.766212919 Simplifying x = -2.766212919

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.141212919, -2.766212919}

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