3x(3x)+2(5)=60x-500

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Solution for 3x(3x)+2(5)=60x-500 equation:


Simplifying
3x(3x) + 2(5) = 60x + -500

Remove parenthesis around (3x)
3x * 3x + 2(5) = 60x + -500

Reorder the terms for easier multiplication:
3 * 3x * x + 2(5) = 60x + -500

Multiply 3 * 3
9x * x + 2(5) = 60x + -500

Multiply x * x
9x2 + 2(5) = 60x + -500

Multiply 2 * 5
9x2 + 10 = 60x + -500

Reorder the terms:
10 + 9x2 = 60x + -500

Reorder the terms:
10 + 9x2 = -500 + 60x

Solving
10 + 9x2 = -500 + 60x

Solving for variable 'x'.

Reorder the terms:
10 + 500 + -60x + 9x2 = -500 + 60x + 500 + -60x

Combine like terms: 10 + 500 = 510
510 + -60x + 9x2 = -500 + 60x + 500 + -60x

Reorder the terms:
510 + -60x + 9x2 = -500 + 500 + 60x + -60x

Combine like terms: -500 + 500 = 0
510 + -60x + 9x2 = 0 + 60x + -60x
510 + -60x + 9x2 = 60x + -60x

Combine like terms: 60x + -60x = 0
510 + -60x + 9x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(170 + -20x + 3x2) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(170 + -20x + 3x2)' equal to zero and attempt to solve: Simplifying 170 + -20x + 3x2 = 0 Solving 170 + -20x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 56.66666667 + -6.666666667x + x2 = 0 Move the constant term to the right: Add '-56.66666667' to each side of the equation. 56.66666667 + -6.666666667x + -56.66666667 + x2 = 0 + -56.66666667 Reorder the terms: 56.66666667 + -56.66666667 + -6.666666667x + x2 = 0 + -56.66666667 Combine like terms: 56.66666667 + -56.66666667 = 0.00000000 0.00000000 + -6.666666667x + x2 = 0 + -56.66666667 -6.666666667x + x2 = 0 + -56.66666667 Combine like terms: 0 + -56.66666667 = -56.66666667 -6.666666667x + x2 = -56.66666667 The x term is -6.666666667x. Take half its coefficient (-3.333333334). Square it (11.11111112) and add it to both sides. Add '11.11111112' to each side of the equation. -6.666666667x + 11.11111112 + x2 = -56.66666667 + 11.11111112 Reorder the terms: 11.11111112 + -6.666666667x + x2 = -56.66666667 + 11.11111112 Combine like terms: -56.66666667 + 11.11111112 = -45.55555555 11.11111112 + -6.666666667x + x2 = -45.55555555 Factor a perfect square on the left side: (x + -3.333333334)(x + -3.333333334) = -45.55555555 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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