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Simplifying 7x2 + 8 = 4x2 + 2(5x + 4) Reorder the terms: 8 + 7x2 = 4x2 + 2(5x + 4) Reorder the terms: 8 + 7x2 = 4x2 + 2(4 + 5x) 8 + 7x2 = 4x2 + (4 * 2 + 5x * 2) 8 + 7x2 = 4x2 + (8 + 10x) Reorder the terms: 8 + 7x2 = 8 + 10x + 4x2 Add '-8' to each side of the equation. 8 + -8 + 7x2 = 8 + 10x + -8 + 4x2 Combine like terms: 8 + -8 = 0 0 + 7x2 = 8 + 10x + -8 + 4x2 7x2 = 8 + 10x + -8 + 4x2 Reorder the terms: 7x2 = 8 + -8 + 10x + 4x2 Combine like terms: 8 + -8 = 0 7x2 = 0 + 10x + 4x2 7x2 = 10x + 4x2 Solving 7x2 = 10x + 4x2 Solving for variable 'x'. Reorder the terms: -10x + 7x2 + -4x2 = 10x + 4x2 + -10x + -4x2 Combine like terms: 7x2 + -4x2 = 3x2 -10x + 3x2 = 10x + 4x2 + -10x + -4x2 Reorder the terms: -10x + 3x2 = 10x + -10x + 4x2 + -4x2 Combine like terms: 10x + -10x = 0 -10x + 3x2 = 0 + 4x2 + -4x2 -10x + 3x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -10x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-10 + 3x) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-10 + 3x)' equal to zero and attempt to solve: Simplifying -10 + 3x = 0 Solving -10 + 3x = 0 Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + 3x = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 3x = 0 + 10 3x = 0 + 10 Combine like terms: 0 + 10 = 10 3x = 10 Divide each side by '3'. x = 3.333333333 Simplifying x = 3.333333333Solution
x = {0, 3.333333333}
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