28x^2-40x+33=81

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Solution for 28x^2-40x+33=81 equation:


Simplifying
28x2 + -40x + 33 = 81

Reorder the terms:
33 + -40x + 28x2 = 81

Solving
33 + -40x + 28x2 = 81

Solving for variable 'x'.

Reorder the terms:
33 + -81 + -40x + 28x2 = 81 + -81

Combine like terms: 33 + -81 = -48
-48 + -40x + 28x2 = 81 + -81

Combine like terms: 81 + -81 = 0
-48 + -40x + 28x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-12 + -10x + 7x2) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(-12 + -10x + 7x2)' equal to zero and attempt to solve: Simplifying -12 + -10x + 7x2 = 0 Solving -12 + -10x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.714285714 + -1.428571429x + x2 = 0 Move the constant term to the right: Add '1.714285714' to each side of the equation. -1.714285714 + -1.428571429x + 1.714285714 + x2 = 0 + 1.714285714 Reorder the terms: -1.714285714 + 1.714285714 + -1.428571429x + x2 = 0 + 1.714285714 Combine like terms: -1.714285714 + 1.714285714 = 0.000000000 0.000000000 + -1.428571429x + x2 = 0 + 1.714285714 -1.428571429x + x2 = 0 + 1.714285714 Combine like terms: 0 + 1.714285714 = 1.714285714 -1.428571429x + x2 = 1.714285714 The x term is -1.428571429x. Take half its coefficient (-0.7142857145). Square it (0.5102040819) and add it to both sides. Add '0.5102040819' to each side of the equation. -1.428571429x + 0.5102040819 + x2 = 1.714285714 + 0.5102040819 Reorder the terms: 0.5102040819 + -1.428571429x + x2 = 1.714285714 + 0.5102040819 Combine like terms: 1.714285714 + 0.5102040819 = 2.2244897959 0.5102040819 + -1.428571429x + x2 = 2.2244897959 Factor a perfect square on the left side: (x + -0.7142857145)(x + -0.7142857145) = 2.2244897959 Calculate the square root of the right side: 1.491472358 Break this problem into two subproblems by setting (x + -0.7142857145) equal to 1.491472358 and -1.491472358.

Subproblem 1

x + -0.7142857145 = 1.491472358 Simplifying x + -0.7142857145 = 1.491472358 Reorder the terms: -0.7142857145 + x = 1.491472358 Solving -0.7142857145 + x = 1.491472358 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7142857145' to each side of the equation. -0.7142857145 + 0.7142857145 + x = 1.491472358 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + x = 1.491472358 + 0.7142857145 x = 1.491472358 + 0.7142857145 Combine like terms: 1.491472358 + 0.7142857145 = 2.2057580725 x = 2.2057580725 Simplifying x = 2.2057580725

Subproblem 2

x + -0.7142857145 = -1.491472358 Simplifying x + -0.7142857145 = -1.491472358 Reorder the terms: -0.7142857145 + x = -1.491472358 Solving -0.7142857145 + x = -1.491472358 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7142857145' to each side of the equation. -0.7142857145 + 0.7142857145 + x = -1.491472358 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + x = -1.491472358 + 0.7142857145 x = -1.491472358 + 0.7142857145 Combine like terms: -1.491472358 + 0.7142857145 = -0.7771866435 x = -0.7771866435 Simplifying x = -0.7771866435

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.2057580725, -0.7771866435}

Solution

x = {2.2057580725, -0.7771866435}

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