16x^2=34x+15

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Solution for 16x^2=34x+15 equation:


Simplifying
16x2 = 34x + 15

Reorder the terms:
16x2 = 15 + 34x

Solving
16x2 = 15 + 34x

Solving for variable 'x'.

Reorder the terms:
-15 + -34x + 16x2 = 15 + 34x + -15 + -34x

Reorder the terms:
-15 + -34x + 16x2 = 15 + -15 + 34x + -34x

Combine like terms: 15 + -15 = 0
-15 + -34x + 16x2 = 0 + 34x + -34x
-15 + -34x + 16x2 = 34x + -34x

Combine like terms: 34x + -34x = 0
-15 + -34x + 16x2 = 0

Factor a trinomial.
(-3 + -8x)(5 + -2x) = 0

Subproblem 1

Set the factor '(-3 + -8x)' equal to zero and attempt to solve: Simplifying -3 + -8x = 0 Solving -3 + -8x = 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 + -8x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -8x = 0 + 3 -8x = 0 + 3 Combine like terms: 0 + 3 = 3 -8x = 3 Divide each side by '-8'. x = -0.375 Simplifying x = -0.375

Subproblem 2

Set the factor '(5 + -2x)' equal to zero and attempt to solve: Simplifying 5 + -2x = 0 Solving 5 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2x = 0 + -5 -2x = 0 + -5 Combine like terms: 0 + -5 = -5 -2x = -5 Divide each side by '-2'. x = 2.5 Simplifying x = 2.5

Solution

x = {-0.375, 2.5}

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