10x^2=9x+7

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Solution for 10x^2=9x+7 equation:


Simplifying
10x2 = 9x + 7

Reorder the terms:
10x2 = 7 + 9x

Solving
10x2 = 7 + 9x

Solving for variable 'x'.

Reorder the terms:
-7 + -9x + 10x2 = 7 + 9x + -7 + -9x

Reorder the terms:
-7 + -9x + 10x2 = 7 + -7 + 9x + -9x

Combine like terms: 7 + -7 = 0
-7 + -9x + 10x2 = 0 + 9x + -9x
-7 + -9x + 10x2 = 9x + -9x

Combine like terms: 9x + -9x = 0
-7 + -9x + 10x2 = 0

Factor a trinomial.
(-1 + -2x)(7 + -5x) = 0

Subproblem 1

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

Subproblem 2

Set the factor '(7 + -5x)' equal to zero and attempt to solve: Simplifying 7 + -5x = 0 Solving 7 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -5x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -5x = 0 + -7 -5x = 0 + -7 Combine like terms: 0 + -7 = -7 -5x = -7 Divide each side by '-5'. x = 1.4 Simplifying x = 1.4

Solution

x = {-0.5, 1.4}

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