=35x^2+61x+24

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Solution for =35x^2+61x+24 equation:


Simplifying
0 = 35x2 + 61x + 24

Reorder the terms:
0 = 24 + 61x + 35x2

Solving
0 = 24 + 61x + 35x2

Solving for variable 'x'.

Combine like terms: 0 + -24 = -24
-24 + -61x + -35x2 = 24 + 61x + 35x2 + -24 + -61x + -35x2

Reorder the terms:
-24 + -61x + -35x2 = 24 + -24 + 61x + -61x + 35x2 + -35x2

Combine like terms: 24 + -24 = 0
-24 + -61x + -35x2 = 0 + 61x + -61x + 35x2 + -35x2
-24 + -61x + -35x2 = 61x + -61x + 35x2 + -35x2

Combine like terms: 61x + -61x = 0
-24 + -61x + -35x2 = 0 + 35x2 + -35x2
-24 + -61x + -35x2 = 35x2 + -35x2

Combine like terms: 35x2 + -35x2 = 0
-24 + -61x + -35x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(24 + 61x + 35x2) = 0

Factor a trinomial.
-1((8 + 7x)(3 + 5x)) = 0

Ignore the factor -1.

Subproblem 1

Set the factor '(8 + 7x)' equal to zero and attempt to solve: Simplifying 8 + 7x = 0 Solving 8 + 7x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + 7x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 7x = 0 + -8 7x = 0 + -8 Combine like terms: 0 + -8 = -8 7x = -8 Divide each side by '7'. x = -1.142857143 Simplifying x = -1.142857143

Subproblem 2

Set the factor '(3 + 5x)' equal to zero and attempt to solve: Simplifying 3 + 5x = 0 Solving 3 + 5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 5x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 5x = 0 + -3 5x = 0 + -3 Combine like terms: 0 + -3 = -3 5x = -3 Divide each side by '5'. x = -0.6 Simplifying x = -0.6

Solution

x = {-1.142857143, -0.6}

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