4x^2-27x+28=-8+7

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Solution for 4x^2-27x+28=-8+7 equation:


Simplifying
4x2 + -27x + 28 = -8 + 7

Reorder the terms:
28 + -27x + 4x2 = -8 + 7

Combine like terms: -8 + 7 = -1
28 + -27x + 4x2 = -1

Solving
28 + -27x + 4x2 = -1

Solving for variable 'x'.

Reorder the terms:
28 + 1 + -27x + 4x2 = -1 + 1

Combine like terms: 28 + 1 = 29
29 + -27x + 4x2 = -1 + 1

Combine like terms: -1 + 1 = 0
29 + -27x + 4x2 = 0

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

Divide each side by '4'.
7.25 + -6.75x + x2 = 0

Move the constant term to the right:

Add '-7.25' to each side of the equation.
7.25 + -6.75x + -7.25 + x2 = 0 + -7.25

Reorder the terms:
7.25 + -7.25 + -6.75x + x2 = 0 + -7.25

Combine like terms: 7.25 + -7.25 = 0.00
0.00 + -6.75x + x2 = 0 + -7.25
-6.75x + x2 = 0 + -7.25

Combine like terms: 0 + -7.25 = -7.25
-6.75x + x2 = -7.25

The x term is -6.75x.  Take half its coefficient (-3.375).
Square it (11.390625) and add it to both sides.

Add '11.390625' to each side of the equation.
-6.75x + 11.390625 + x2 = -7.25 + 11.390625

Reorder the terms:
11.390625 + -6.75x + x2 = -7.25 + 11.390625

Combine like terms: -7.25 + 11.390625 = 4.140625
11.390625 + -6.75x + x2 = 4.140625

Factor a perfect square on the left side:
(x + -3.375)(x + -3.375) = 4.140625

Calculate the square root of the right side: 2.034852575

Break this problem into two subproblems by setting 
(x + -3.375) equal to 2.034852575 and -2.034852575.

Subproblem 1

x + -3.375 = 2.034852575 Simplifying x + -3.375 = 2.034852575 Reorder the terms: -3.375 + x = 2.034852575 Solving -3.375 + x = 2.034852575 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.375' to each side of the equation. -3.375 + 3.375 + x = 2.034852575 + 3.375 Combine like terms: -3.375 + 3.375 = 0.000 0.000 + x = 2.034852575 + 3.375 x = 2.034852575 + 3.375 Combine like terms: 2.034852575 + 3.375 = 5.409852575 x = 5.409852575 Simplifying x = 5.409852575

Subproblem 2

x + -3.375 = -2.034852575 Simplifying x + -3.375 = -2.034852575 Reorder the terms: -3.375 + x = -2.034852575 Solving -3.375 + x = -2.034852575 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.375' to each side of the equation. -3.375 + 3.375 + x = -2.034852575 + 3.375 Combine like terms: -3.375 + 3.375 = 0.000 0.000 + x = -2.034852575 + 3.375 x = -2.034852575 + 3.375 Combine like terms: -2.034852575 + 3.375 = 1.340147425 x = 1.340147425 Simplifying x = 1.340147425

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.409852575, 1.340147425}

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