10x^2=-13x+9

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Solution for 10x^2=-13x+9 equation:


Simplifying
10x2 = -13x + 9

Reorder the terms:
10x2 = 9 + -13x

Solving
10x2 = 9 + -13x

Solving for variable 'x'.

Reorder the terms:
-9 + 13x + 10x2 = 9 + -13x + -9 + 13x

Reorder the terms:
-9 + 13x + 10x2 = 9 + -9 + -13x + 13x

Combine like terms: 9 + -9 = 0
-9 + 13x + 10x2 = 0 + -13x + 13x
-9 + 13x + 10x2 = -13x + 13x

Combine like terms: -13x + 13x = 0
-9 + 13x + 10x2 = 0

Factor a trinomial.
(-9 + -5x)(1 + -2x) = 0

Subproblem 1

Set the factor '(-9 + -5x)' equal to zero and attempt to solve: Simplifying -9 + -5x = 0 Solving -9 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -5x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -5x = 0 + 9 -5x = 0 + 9 Combine like terms: 0 + 9 = 9 -5x = 9 Divide each side by '-5'. x = -1.8 Simplifying x = -1.8

Subproblem 2

Set the factor '(1 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Divide each side by '-2'. x = 0.5 Simplifying x = 0.5

Solution

x = {-1.8, 0.5}

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