(-9x+8)x+7x(1x+10)-3=

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Solution for (-9x+8)x+7x(1x+10)-3= equation:


Simplifying
(-9x + 8) * x + 7x(1x + 10) + -3 = 0

Reorder the terms:
(8 + -9x) * x + 7x(1x + 10) + -3 = 0

Reorder the terms for easier multiplication:
x(8 + -9x) + 7x(1x + 10) + -3 = 0
(8 * x + -9x * x) + 7x(1x + 10) + -3 = 0
(8x + -9x2) + 7x(1x + 10) + -3 = 0

Reorder the terms:
8x + -9x2 + 7x(10 + 1x) + -3 = 0
8x + -9x2 + (10 * 7x + 1x * 7x) + -3 = 0
8x + -9x2 + (70x + 7x2) + -3 = 0

Reorder the terms:
-3 + 8x + 70x + -9x2 + 7x2 = 0

Combine like terms: 8x + 70x = 78x
-3 + 78x + -9x2 + 7x2 = 0

Combine like terms: -9x2 + 7x2 = -2x2
-3 + 78x + -2x2 = 0

Solving
-3 + 78x + -2x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
1.5 + -39x + x2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + -39x + -1.5 + x2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + -39x + x2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + -39x + x2 = 0 + -1.5
-39x + x2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
-39x + x2 = -1.5

The x term is -39x.  Take half its coefficient (-19.5).
Square it (380.25) and add it to both sides.

Add '380.25' to each side of the equation.
-39x + 380.25 + x2 = -1.5 + 380.25

Reorder the terms:
380.25 + -39x + x2 = -1.5 + 380.25

Combine like terms: -1.5 + 380.25 = 378.75
380.25 + -39x + x2 = 378.75

Factor a perfect square on the left side:
(x + -19.5)(x + -19.5) = 378.75

Calculate the square root of the right side: 19.461500456

Break this problem into two subproblems by setting 
(x + -19.5) equal to 19.461500456 and -19.461500456.

Subproblem 1

x + -19.5 = 19.461500456 Simplifying x + -19.5 = 19.461500456 Reorder the terms: -19.5 + x = 19.461500456 Solving -19.5 + x = 19.461500456 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '19.5' to each side of the equation. -19.5 + 19.5 + x = 19.461500456 + 19.5 Combine like terms: -19.5 + 19.5 = 0.0 0.0 + x = 19.461500456 + 19.5 x = 19.461500456 + 19.5 Combine like terms: 19.461500456 + 19.5 = 38.961500456 x = 38.961500456 Simplifying x = 38.961500456

Subproblem 2

x + -19.5 = -19.461500456 Simplifying x + -19.5 = -19.461500456 Reorder the terms: -19.5 + x = -19.461500456 Solving -19.5 + x = -19.461500456 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '19.5' to each side of the equation. -19.5 + 19.5 + x = -19.461500456 + 19.5 Combine like terms: -19.5 + 19.5 = 0.0 0.0 + x = -19.461500456 + 19.5 x = -19.461500456 + 19.5 Combine like terms: -19.461500456 + 19.5 = 0.038499544 x = 0.038499544 Simplifying x = 0.038499544

Solution

The solution to the problem is based on the solutions from the subproblems. x = {38.961500456, 0.038499544}

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