18x^2-48x+16=0

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Solution for 18x^2-48x+16=0 equation:


Simplifying
18x2 + -48x + 16 = 0

Reorder the terms:
16 + -48x + 18x2 = 0

Solving
16 + -48x + 18x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(8 + -24x + 9x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(8 + -24x + 9x2)' equal to zero and attempt to solve: Simplifying 8 + -24x + 9x2 = 0 Solving 8 + -24x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.8888888889 + -2.666666667x + x2 = 0 Move the constant term to the right: Add '-0.8888888889' to each side of the equation. 0.8888888889 + -2.666666667x + -0.8888888889 + x2 = 0 + -0.8888888889 Reorder the terms: 0.8888888889 + -0.8888888889 + -2.666666667x + x2 = 0 + -0.8888888889 Combine like terms: 0.8888888889 + -0.8888888889 = 0.0000000000 0.0000000000 + -2.666666667x + x2 = 0 + -0.8888888889 -2.666666667x + x2 = 0 + -0.8888888889 Combine like terms: 0 + -0.8888888889 = -0.8888888889 -2.666666667x + x2 = -0.8888888889 The x term is -2.666666667x. Take half its coefficient (-1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. -2.666666667x + 1.777777780 + x2 = -0.8888888889 + 1.777777780 Reorder the terms: 1.777777780 + -2.666666667x + x2 = -0.8888888889 + 1.777777780 Combine like terms: -0.8888888889 + 1.777777780 = 0.8888888911 1.777777780 + -2.666666667x + x2 = 0.8888888911 Factor a perfect square on the left side: (x + -1.333333334)(x + -1.333333334) = 0.8888888911 Calculate the square root of the right side: 0.942809043 Break this problem into two subproblems by setting (x + -1.333333334) equal to 0.942809043 and -0.942809043.

Subproblem 1

x + -1.333333334 = 0.942809043 Simplifying x + -1.333333334 = 0.942809043 Reorder the terms: -1.333333334 + x = 0.942809043 Solving -1.333333334 + x = 0.942809043 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.333333334' to each side of the equation. -1.333333334 + 1.333333334 + x = 0.942809043 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = 0.942809043 + 1.333333334 x = 0.942809043 + 1.333333334 Combine like terms: 0.942809043 + 1.333333334 = 2.276142377 x = 2.276142377 Simplifying x = 2.276142377

Subproblem 2

x + -1.333333334 = -0.942809043 Simplifying x + -1.333333334 = -0.942809043 Reorder the terms: -1.333333334 + x = -0.942809043 Solving -1.333333334 + x = -0.942809043 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.333333334' to each side of the equation. -1.333333334 + 1.333333334 + x = -0.942809043 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = -0.942809043 + 1.333333334 x = -0.942809043 + 1.333333334 Combine like terms: -0.942809043 + 1.333333334 = 0.390524291 x = 0.390524291 Simplifying x = 0.390524291

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.276142377, 0.390524291}

Solution

x = {2.276142377, 0.390524291}

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