4x^2=9x+10

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Solution for 4x^2=9x+10 equation:


Simplifying
4x2 = 9x + 10

Reorder the terms:
4x2 = 10 + 9x

Solving
4x2 = 10 + 9x

Solving for variable 'x'.

Reorder the terms:
-10 + -9x + 4x2 = 10 + 9x + -10 + -9x

Reorder the terms:
-10 + -9x + 4x2 = 10 + -10 + 9x + -9x

Combine like terms: 10 + -10 = 0
-10 + -9x + 4x2 = 0 + 9x + -9x
-10 + -9x + 4x2 = 9x + -9x

Combine like terms: 9x + -9x = 0
-10 + -9x + 4x2 = 0

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

Divide each side by '4'.
-2.5 + -2.25x + x2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + -2.25x + 2.5 + x2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + -2.25x + x2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + -2.25x + x2 = 0 + 2.5
-2.25x + x2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
-2.25x + x2 = 2.5

The x term is -2.25x.  Take half its coefficient (-1.125).
Square it (1.265625) and add it to both sides.

Add '1.265625' to each side of the equation.
-2.25x + 1.265625 + x2 = 2.5 + 1.265625

Reorder the terms:
1.265625 + -2.25x + x2 = 2.5 + 1.265625

Combine like terms: 2.5 + 1.265625 = 3.765625
1.265625 + -2.25x + x2 = 3.765625

Factor a perfect square on the left side:
(x + -1.125)(x + -1.125) = 3.765625

Calculate the square root of the right side: 1.940521837

Break this problem into two subproblems by setting 
(x + -1.125) equal to 1.940521837 and -1.940521837.

Subproblem 1

x + -1.125 = 1.940521837 Simplifying x + -1.125 = 1.940521837 Reorder the terms: -1.125 + x = 1.940521837 Solving -1.125 + x = 1.940521837 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + x = 1.940521837 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x = 1.940521837 + 1.125 x = 1.940521837 + 1.125 Combine like terms: 1.940521837 + 1.125 = 3.065521837 x = 3.065521837 Simplifying x = 3.065521837

Subproblem 2

x + -1.125 = -1.940521837 Simplifying x + -1.125 = -1.940521837 Reorder the terms: -1.125 + x = -1.940521837 Solving -1.125 + x = -1.940521837 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + x = -1.940521837 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x = -1.940521837 + 1.125 x = -1.940521837 + 1.125 Combine like terms: -1.940521837 + 1.125 = -0.815521837 x = -0.815521837 Simplifying x = -0.815521837

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.065521837, -0.815521837}

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