5x^2(6+4)-3x(9+5)=36

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Solution for 5x^2(6+4)-3x(9+5)=36 equation:


Simplifying
5x2(6 + 4) + -3x(9 + 5) = 36

Combine like terms: 6 + 4 = 10
5x2(10) + -3x(9 + 5) = 36

Reorder the terms for easier multiplication:
5 * 10x2 + -3x(9 + 5) = 36

Multiply 5 * 10
50x2 + -3x(9 + 5) = 36

Combine like terms: 9 + 5 = 14
50x2 + -3x(14) = 36

Reorder the terms for easier multiplication:
50x2 + -3 * 14x = 36

Multiply -3 * 14
50x2 + -42x = 36

Reorder the terms:
-42x + 50x2 = 36

Solving
-42x + 50x2 = 36

Solving for variable 'x'.

Reorder the terms:
-36 + -42x + 50x2 = 36 + -36

Combine like terms: 36 + -36 = 0
-36 + -42x + 50x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-18 + -21x + 25x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-18 + -21x + 25x2)' equal to zero and attempt to solve: Simplifying -18 + -21x + 25x2 = 0 Solving -18 + -21x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.72 + -0.84x + x2 = 0 Move the constant term to the right: Add '0.72' to each side of the equation. -0.72 + -0.84x + 0.72 + x2 = 0 + 0.72 Reorder the terms: -0.72 + 0.72 + -0.84x + x2 = 0 + 0.72 Combine like terms: -0.72 + 0.72 = 0.00 0.00 + -0.84x + x2 = 0 + 0.72 -0.84x + x2 = 0 + 0.72 Combine like terms: 0 + 0.72 = 0.72 -0.84x + x2 = 0.72 The x term is -0.84x. Take half its coefficient (-0.42). Square it (0.1764) and add it to both sides. Add '0.1764' to each side of the equation. -0.84x + 0.1764 + x2 = 0.72 + 0.1764 Reorder the terms: 0.1764 + -0.84x + x2 = 0.72 + 0.1764 Combine like terms: 0.72 + 0.1764 = 0.8964 0.1764 + -0.84x + x2 = 0.8964 Factor a perfect square on the left side: (x + -0.42)(x + -0.42) = 0.8964 Calculate the square root of the right side: 0.94678403 Break this problem into two subproblems by setting (x + -0.42) equal to 0.94678403 and -0.94678403.

Subproblem 1

x + -0.42 = 0.94678403 Simplifying x + -0.42 = 0.94678403 Reorder the terms: -0.42 + x = 0.94678403 Solving -0.42 + x = 0.94678403 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.42' to each side of the equation. -0.42 + 0.42 + x = 0.94678403 + 0.42 Combine like terms: -0.42 + 0.42 = 0.00 0.00 + x = 0.94678403 + 0.42 x = 0.94678403 + 0.42 Combine like terms: 0.94678403 + 0.42 = 1.36678403 x = 1.36678403 Simplifying x = 1.36678403

Subproblem 2

x + -0.42 = -0.94678403 Simplifying x + -0.42 = -0.94678403 Reorder the terms: -0.42 + x = -0.94678403 Solving -0.42 + x = -0.94678403 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.42' to each side of the equation. -0.42 + 0.42 + x = -0.94678403 + 0.42 Combine like terms: -0.42 + 0.42 = 0.00 0.00 + x = -0.94678403 + 0.42 x = -0.94678403 + 0.42 Combine like terms: -0.94678403 + 0.42 = -0.52678403 x = -0.52678403 Simplifying x = -0.52678403

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.36678403, -0.52678403}

Solution

x = {1.36678403, -0.52678403}

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