x=-9x^2+42x+10

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Solution for x=-9x^2+42x+10 equation:


Simplifying
x = -9x2 + 42x + 10

Reorder the terms:
x = 10 + 42x + -9x2

Solving
x = 10 + 42x + -9x2

Solving for variable 'x'.

Reorder the terms:
-10 + x + -42x + 9x2 = 10 + 42x + -9x2 + -10 + -42x + 9x2

Combine like terms: x + -42x = -41x
-10 + -41x + 9x2 = 10 + 42x + -9x2 + -10 + -42x + 9x2

Reorder the terms:
-10 + -41x + 9x2 = 10 + -10 + 42x + -42x + -9x2 + 9x2

Combine like terms: 10 + -10 = 0
-10 + -41x + 9x2 = 0 + 42x + -42x + -9x2 + 9x2
-10 + -41x + 9x2 = 42x + -42x + -9x2 + 9x2

Combine like terms: 42x + -42x = 0
-10 + -41x + 9x2 = 0 + -9x2 + 9x2
-10 + -41x + 9x2 = -9x2 + 9x2

Combine like terms: -9x2 + 9x2 = 0
-10 + -41x + 9x2 = 0

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

Divide each side by '9'.
-1.111111111 + -4.555555556x + x2 = 0

Move the constant term to the right:

Add '1.111111111' to each side of the equation.
-1.111111111 + -4.555555556x + 1.111111111 + x2 = 0 + 1.111111111

Reorder the terms:
-1.111111111 + 1.111111111 + -4.555555556x + x2 = 0 + 1.111111111

Combine like terms: -1.111111111 + 1.111111111 = 0.000000000
0.000000000 + -4.555555556x + x2 = 0 + 1.111111111
-4.555555556x + x2 = 0 + 1.111111111

Combine like terms: 0 + 1.111111111 = 1.111111111
-4.555555556x + x2 = 1.111111111

The x term is -4.555555556x.  Take half its coefficient (-2.277777778).
Square it (5.188271606) and add it to both sides.

Add '5.188271606' to each side of the equation.
-4.555555556x + 5.188271606 + x2 = 1.111111111 + 5.188271606

Reorder the terms:
5.188271606 + -4.555555556x + x2 = 1.111111111 + 5.188271606

Combine like terms: 1.111111111 + 5.188271606 = 6.299382717
5.188271606 + -4.555555556x + x2 = 6.299382717

Factor a perfect square on the left side:
(x + -2.277777778)(x + -2.277777778) = 6.299382717

Calculate the square root of the right side: 2.509857111

Break this problem into two subproblems by setting 
(x + -2.277777778) equal to 2.509857111 and -2.509857111.

Subproblem 1

x + -2.277777778 = 2.509857111 Simplifying x + -2.277777778 = 2.509857111 Reorder the terms: -2.277777778 + x = 2.509857111 Solving -2.277777778 + x = 2.509857111 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.277777778' to each side of the equation. -2.277777778 + 2.277777778 + x = 2.509857111 + 2.277777778 Combine like terms: -2.277777778 + 2.277777778 = 0.000000000 0.000000000 + x = 2.509857111 + 2.277777778 x = 2.509857111 + 2.277777778 Combine like terms: 2.509857111 + 2.277777778 = 4.787634889 x = 4.787634889 Simplifying x = 4.787634889

Subproblem 2

x + -2.277777778 = -2.509857111 Simplifying x + -2.277777778 = -2.509857111 Reorder the terms: -2.277777778 + x = -2.509857111 Solving -2.277777778 + x = -2.509857111 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.277777778' to each side of the equation. -2.277777778 + 2.277777778 + x = -2.509857111 + 2.277777778 Combine like terms: -2.277777778 + 2.277777778 = 0.000000000 0.000000000 + x = -2.509857111 + 2.277777778 x = -2.509857111 + 2.277777778 Combine like terms: -2.509857111 + 2.277777778 = -0.232079333 x = -0.232079333 Simplifying x = -0.232079333

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.787634889, -0.232079333}

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