5x+10=3x(3+4x)

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Solution for 5x+10=3x(3+4x) equation:


Simplifying
5x + 10 = 3x(3 + 4x)

Reorder the terms:
10 + 5x = 3x(3 + 4x)
10 + 5x = (3 * 3x + 4x * 3x)
10 + 5x = (9x + 12x2)

Solving
10 + 5x = 9x + 12x2

Solving for variable 'x'.

Combine like terms: 5x + -9x = -4x
10 + -4x + -12x2 = 9x + 12x2 + -9x + -12x2

Reorder the terms:
10 + -4x + -12x2 = 9x + -9x + 12x2 + -12x2

Combine like terms: 9x + -9x = 0
10 + -4x + -12x2 = 0 + 12x2 + -12x2
10 + -4x + -12x2 = 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
10 + -4x + -12x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + -2x + -6x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(5 + -2x + -6x2)' equal to zero and attempt to solve: Simplifying 5 + -2x + -6x2 = 0 Solving 5 + -2x + -6x2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -0.8333333333 + 0.3333333333x + x2 = 0 Move the constant term to the right: Add '0.8333333333' to each side of the equation. -0.8333333333 + 0.3333333333x + 0.8333333333 + x2 = 0 + 0.8333333333 Reorder the terms: -0.8333333333 + 0.8333333333 + 0.3333333333x + x2 = 0 + 0.8333333333 Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000 0.0000000000 + 0.3333333333x + x2 = 0 + 0.8333333333 0.3333333333x + x2 = 0 + 0.8333333333 Combine like terms: 0 + 0.8333333333 = 0.8333333333 0.3333333333x + x2 = 0.8333333333 The x term is 0.3333333333x. Take half its coefficient (0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. 0.3333333333x + 0.02777777779 + x2 = 0.8333333333 + 0.02777777779 Reorder the terms: 0.02777777779 + 0.3333333333x + x2 = 0.8333333333 + 0.02777777779 Combine like terms: 0.8333333333 + 0.02777777779 = 0.86111111109 0.02777777779 + 0.3333333333x + x2 = 0.86111111109 Factor a perfect square on the left side: (x + 0.1666666667)(x + 0.1666666667) = 0.86111111109 Calculate the square root of the right side: 0.927960727 Break this problem into two subproblems by setting (x + 0.1666666667) equal to 0.927960727 and -0.927960727.

Subproblem 1

x + 0.1666666667 = 0.927960727 Simplifying x + 0.1666666667 = 0.927960727 Reorder the terms: 0.1666666667 + x = 0.927960727 Solving 0.1666666667 + x = 0.927960727 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1666666667' to each side of the equation. 0.1666666667 + -0.1666666667 + x = 0.927960727 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = 0.927960727 + -0.1666666667 x = 0.927960727 + -0.1666666667 Combine like terms: 0.927960727 + -0.1666666667 = 0.7612940603 x = 0.7612940603 Simplifying x = 0.7612940603

Subproblem 2

x + 0.1666666667 = -0.927960727 Simplifying x + 0.1666666667 = -0.927960727 Reorder the terms: 0.1666666667 + x = -0.927960727 Solving 0.1666666667 + x = -0.927960727 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1666666667' to each side of the equation. 0.1666666667 + -0.1666666667 + x = -0.927960727 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = -0.927960727 + -0.1666666667 x = -0.927960727 + -0.1666666667 Combine like terms: -0.927960727 + -0.1666666667 = -1.0946273937 x = -1.0946273937 Simplifying x = -1.0946273937

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.7612940603, -1.0946273937}

Solution

x = {0.7612940603, -1.0946273937}

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