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Simplifying H(x) = 6x2 + -30x Multiply H * x xH = 6x2 + -30x Reorder the terms: xH = -30x + 6x2 Solving xH = -30x + 6x2 Solving for variable 'x'. Reorder the terms: 30x + xH + -6x2 = -30x + 6x2 + 30x + -6x2 Reorder the terms: 30x + xH + -6x2 = -30x + 30x + 6x2 + -6x2 Combine like terms: -30x + 30x = 0 30x + xH + -6x2 = 0 + 6x2 + -6x2 30x + xH + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 30x + xH + -6x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(30 + H + -6x) = 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 '(30 + H + -6x)' equal to zero and attempt to solve: Simplifying 30 + H + -6x = 0 Solving 30 + H + -6x = 0 Move all terms containing x to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + H + -30 + -6x = 0 + -30 Reorder the terms: 30 + -30 + H + -6x = 0 + -30 Combine like terms: 30 + -30 = 0 0 + H + -6x = 0 + -30 H + -6x = 0 + -30 Combine like terms: 0 + -30 = -30 H + -6x = -30 Add '-1H' to each side of the equation. H + -1H + -6x = -30 + -1H Combine like terms: H + -1H = 0 0 + -6x = -30 + -1H -6x = -30 + -1H Divide each side by '-6'. x = 5 + 0.1666666667H Simplifying x = 5 + 0.1666666667HSolution
x = {0, 5 + 0.1666666667H}
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