4x^2-25x+23=-9x+18

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Solution for 4x^2-25x+23=-9x+18 equation:


Simplifying
4x2 + -25x + 23 = -9x + 18

Reorder the terms:
23 + -25x + 4x2 = -9x + 18

Reorder the terms:
23 + -25x + 4x2 = 18 + -9x

Solving
23 + -25x + 4x2 = 18 + -9x

Solving for variable 'x'.

Reorder the terms:
23 + -18 + -25x + 9x + 4x2 = 18 + -9x + -18 + 9x

Combine like terms: 23 + -18 = 5
5 + -25x + 9x + 4x2 = 18 + -9x + -18 + 9x

Combine like terms: -25x + 9x = -16x
5 + -16x + 4x2 = 18 + -9x + -18 + 9x

Reorder the terms:
5 + -16x + 4x2 = 18 + -18 + -9x + 9x

Combine like terms: 18 + -18 = 0
5 + -16x + 4x2 = 0 + -9x + 9x
5 + -16x + 4x2 = -9x + 9x

Combine like terms: -9x + 9x = 0
5 + -16x + 4x2 = 0

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

Divide each side by '4'.
1.25 + -4x + x2 = 0

Move the constant term to the right:

Add '-1.25' to each side of the equation.
1.25 + -4x + -1.25 + x2 = 0 + -1.25

Reorder the terms:
1.25 + -1.25 + -4x + x2 = 0 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + -4x + x2 = 0 + -1.25
-4x + x2 = 0 + -1.25

Combine like terms: 0 + -1.25 = -1.25
-4x + x2 = -1.25

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = -1.25 + 4

Reorder the terms:
4 + -4x + x2 = -1.25 + 4

Combine like terms: -1.25 + 4 = 2.75
4 + -4x + x2 = 2.75

Factor a perfect square on the left side:
(x + -2)(x + -2) = 2.75

Calculate the square root of the right side: 1.658312395

Break this problem into two subproblems by setting 
(x + -2) equal to 1.658312395 and -1.658312395.

Subproblem 1

x + -2 = 1.658312395 Simplifying x + -2 = 1.658312395 Reorder the terms: -2 + x = 1.658312395 Solving -2 + x = 1.658312395 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 1.658312395 + 2 Combine like terms: -2 + 2 = 0 0 + x = 1.658312395 + 2 x = 1.658312395 + 2 Combine like terms: 1.658312395 + 2 = 3.658312395 x = 3.658312395 Simplifying x = 3.658312395

Subproblem 2

x + -2 = -1.658312395 Simplifying x + -2 = -1.658312395 Reorder the terms: -2 + x = -1.658312395 Solving -2 + x = -1.658312395 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -1.658312395 + 2 Combine like terms: -2 + 2 = 0 0 + x = -1.658312395 + 2 x = -1.658312395 + 2 Combine like terms: -1.658312395 + 2 = 0.341687605 x = 0.341687605 Simplifying x = 0.341687605

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.658312395, 0.341687605}

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