4(3x+5)(3x+5)=13

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Solution for 4(3x+5)(3x+5)=13 equation:


Simplifying
4(3x + 5)(3x + 5) = 13

Reorder the terms:
4(5 + 3x)(3x + 5) = 13

Reorder the terms:
4(5 + 3x)(5 + 3x) = 13

Multiply (5 + 3x) * (5 + 3x)
4(5(5 + 3x) + 3x * (5 + 3x)) = 13
4((5 * 5 + 3x * 5) + 3x * (5 + 3x)) = 13
4((25 + 15x) + 3x * (5 + 3x)) = 13
4(25 + 15x + (5 * 3x + 3x * 3x)) = 13
4(25 + 15x + (15x + 9x2)) = 13

Combine like terms: 15x + 15x = 30x
4(25 + 30x + 9x2) = 13
(25 * 4 + 30x * 4 + 9x2 * 4) = 13
(100 + 120x + 36x2) = 13

Solving
100 + 120x + 36x2 = 13

Solving for variable 'x'.

Reorder the terms:
100 + -13 + 120x + 36x2 = 13 + -13

Combine like terms: 100 + -13 = 87
87 + 120x + 36x2 = 13 + -13

Combine like terms: 13 + -13 = 0
87 + 120x + 36x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(29 + 40x + 12x2) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(29 + 40x + 12x2)' equal to zero and attempt to solve: Simplifying 29 + 40x + 12x2 = 0 Solving 29 + 40x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 2.416666667 + 3.333333333x + x2 = 0 Move the constant term to the right: Add '-2.416666667' to each side of the equation. 2.416666667 + 3.333333333x + -2.416666667 + x2 = 0 + -2.416666667 Reorder the terms: 2.416666667 + -2.416666667 + 3.333333333x + x2 = 0 + -2.416666667 Combine like terms: 2.416666667 + -2.416666667 = 0.000000000 0.000000000 + 3.333333333x + x2 = 0 + -2.416666667 3.333333333x + x2 = 0 + -2.416666667 Combine like terms: 0 + -2.416666667 = -2.416666667 3.333333333x + x2 = -2.416666667 The x term is 3.333333333x. Take half its coefficient (1.666666667). Square it (2.777777779) and add it to both sides. Add '2.777777779' to each side of the equation. 3.333333333x + 2.777777779 + x2 = -2.416666667 + 2.777777779 Reorder the terms: 2.777777779 + 3.333333333x + x2 = -2.416666667 + 2.777777779 Combine like terms: -2.416666667 + 2.777777779 = 0.361111112 2.777777779 + 3.333333333x + x2 = 0.361111112 Factor a perfect square on the left side: (x + 1.666666667)(x + 1.666666667) = 0.361111112 Calculate the square root of the right side: 0.600925213 Break this problem into two subproblems by setting (x + 1.666666667) equal to 0.600925213 and -0.600925213.

Subproblem 1

x + 1.666666667 = 0.600925213 Simplifying x + 1.666666667 = 0.600925213 Reorder the terms: 1.666666667 + x = 0.600925213 Solving 1.666666667 + x = 0.600925213 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.666666667' to each side of the equation. 1.666666667 + -1.666666667 + x = 0.600925213 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + x = 0.600925213 + -1.666666667 x = 0.600925213 + -1.666666667 Combine like terms: 0.600925213 + -1.666666667 = -1.065741454 x = -1.065741454 Simplifying x = -1.065741454

Subproblem 2

x + 1.666666667 = -0.600925213 Simplifying x + 1.666666667 = -0.600925213 Reorder the terms: 1.666666667 + x = -0.600925213 Solving 1.666666667 + x = -0.600925213 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.666666667' to each side of the equation. 1.666666667 + -1.666666667 + x = -0.600925213 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + x = -0.600925213 + -1.666666667 x = -0.600925213 + -1.666666667 Combine like terms: -0.600925213 + -1.666666667 = -2.26759188 x = -2.26759188 Simplifying x = -2.26759188

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-1.065741454, -2.26759188}

Solution

x = {-1.065741454, -2.26759188}

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